How To Find The Domain of a Function - Radicals, Fractions & Square Roots - Interval Notation
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- čas přidán 7. 09. 2017
- This algebra video tutorial explains how to find the domain of a function that contains radicals, fractions, and square roots in the denominator using interval notation.
Functions and Graphs Practice Test: • Functions and Graphs |...
Transformations of Functions:
• Transformations of Fun...
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How To Find The Range of a Function:
• How To Find The Range ...
Domain and Range - More Examples:
• Domain and Range Funct...
Domain and Range From a Graph:
• Domain and Range of a ...
____________________________________________
Domain and Range - Radical Functions:
• Domain of a Square Roo...
Domain of Logarithmic Functions:
• How To Find The Domain...
Domain and Range - Piecewise Functions:
• Graphing Piecewise Fun...
Domain and Range - Inverse Functions:
• How To Find The Domain...
_____________________________________________
SAT Math Test Prep:
• Evaluating Functions a...
ACT Math Test Prep:
• ACT Math Test Prep
Final Exams and Video Playlists:
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Functions and Graphs: czcams.com/video/ZTEv8OnGaxo/video.html
Transformations of Functions: czcams.com/video/tyQLp6x-GoU/video.html
Graphing Polynomial Functions: czcams.com/video/rOOefdqMvtA/video.html
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Koooko🤍🤍🤍🤍🤍🤍🤍🤍🤍🤍🤍😘kko. 😭😘😘
why cant u be my professor in college :(
Well you are my professor on my college tyty!
@@VanQuishMk HA
I just noticed this. CZcamsrs are really good at explaining lessons because there is a "necessity" to do so. If they suck, no one will watch them and they gain no incentive. Unlike your school teachers, they are already "paid", so whether they give their best every lesson is, well, basically an option. Plus teachers are humans, they get tired from teaching all day, which decreases their performances.
But of course, there are really good school teachers out there.
Hell your right!
Yea but CZcams teachers cant mentor you, see where your making mistakes and test your knowledge. The connection is necessary.
You should notice the ones who aren't getting viewers. They exist.
Nah! i don't it's all teachers that do so
Faxxx
God bless you for this. i was literally in tears yesterday when i got to class and was the only one who didn't understand
Please help me at 3:20 how hi find (x-4)(x-5)
Salim Amer how hi?
@@velix5390 by "hi", Salim means "he"
Salim Amer have you learned quadratic equations ? Your teacher should have thought this in 8th
@@salimamer6660 i dont know how if you have found your answer but (x-5) (x-4) is from factorizing x² - 9x +20. you can always use your casio calculator to factorize if you find it difficult, or watch a video on factorization
It’s nice to see that people share the common problem that they have professors that don’t explain things well. My lecture in precalculus is almost 2 hours and I end up leaving more confused than coming in. And I’m going back to school after 9 years. I really was about to give up after flunking my first test but I found these videos and I can’t believe how simple you put things into perspective. My professor teaches us as if this is as easy for us as it is for him. Thank you so much and good luck to everyone else out there kicking butt in school!
I would just try to forget what my professor told us if it sounded horribly confusing, then read some books about it instead.
I’m taking precalculus right now, and my lecture is also 2 hours and I’m so confused right now. My professor goes through the lectures pretty fast, that I don’t even have enough time to process the information. I’m barely entering my 3rd week of college and I’m already confused. I have a quiz coming up, so I’m trying my best to study right now.
I have a unit test coming up in precalc with everything we’ve learned so far in the unit… it’s a lot so I hope I do well
I'm 16 grade 11 in India and I usually go for videos in my native language but oh my my.. your explanations are so clear that language is not a botheration anymore.. subscribed 👍
He also speaks in a much more professional manner
Like some CZcams teachers try to push in too much enthusiasm, or are just forcing out the words to be clear. They trie out themselves, as well as the audience.
He is a lot better in that regard.
Same here
From India too
Yup same case👍
@@MP-cv6if it's not necessarily that he's more professional, but rather he's more straightforward. He knows how to talk in such a way that even those unfamiliar with the concept come to understand it, which is exactly what you want out of a teacher. He goes through everything methodically so that you understand, unlike some math teachers that assume you just know everything so they skip over some steps. And while it's kind of justified as they taught you this stuff before and the YT vids have to assume you aren't familiar; it's not as if you remember everything taught to you from 3 grade levels ago.
Same same! I've got my exams today and I'm watching this video suddenly my life feels much better.
My professor teaches like we have a PhD in mathematics in my pre-calculus class. You should see me in class I'm like a philosopher just questioning the meaning of life. What has life become lol
I am now sitting in class watching this video trying to learn, and I have just read out your comment to the class and to the teacher!
Same problem, per-calculus. I feel like I am overwhelmed.
In what college do you study?
@@hanf4415 Lone Star college
deadass. in 11th grade in hs and my pre calc teacher doesnt teach us. we have to be self taught by the textbook, but its a shitty textbook.
Do you know how happy I feel? Do you know how much I"ve improved by now? Everything is thanks to you, you're the best teacher I never had. I hope I can mail you some thank you stuff!!! THANK YOU SO MUCH!!!! I LOVE THE WAY YOU TEACH!!
Seokjnnie Jinjara ARMYYY
@@Cyra7 yayyy armyy
@Dm Wreath You cant have a negative inside a root because that would make it an imaginary number. Think of a number that is negative after being squared. There isn't any. That is why you need to have only positive numbers inside a root sign. Look up 'complex numbers' to know more.
Plus1
SEOKJINN lessgaurr
The best explanation of this topic ever. I am a university student who has been struggling to understand this topic since school, and you made years of struggle go away in 18 minutes. Also, to everyone writing an exam, YOU GOT THIS
Thank you! You too!
Remembering my University years back in 1984. With this type of explaining, we could passed those exams way more easy. Excellent my friend
You are just very right
You are just very right
How come my teacher gotta take a whole 50 minutes and still unclear, and this dude explained it perfectly and to the point in under 20 minutes.
Practice, experimentation and dedication.
Same here!!!!!? 😂😂😂😂
Same buddy!
My teacher scratches his balls or 50 min. I start to think that even he doesnt know how to do the problems whit how many mistakes he has made doing one.
@@fabtube7177 I cant see why they complain about not getting paid enough, 90% of them are as useful as getting hit on the head with a rock. This makes me so furious
im learning more from youtube videos than my professor smh
mikeyv1 I’m in 10th grade I’m learning this
JustSpwnz - 12th
The Legend it is 12 th grade but I’m on my last year on math
smallworkz.com
czcams.com/video/gLLa7fvmIHk/video.html
y’all talkin bout how you guys are learning this in college, i’m in 8th grade why tf are they teaching me this
Ohh I see. Domains were also introduced to us last year ( I was on 8th grade). I didn't understand much so I'm recalling apparently.
Ok I’ll elaborate. You learn this in 7th grade or 6th grade but it comes up again with more difficult topics. I’m using this in calculus to find the domain of logarithmic functions and trigs. Most people forget or they just have to use it but in a harder way.
@@mikuculus3720 yep exactly
wow we r learning this only in 11th. Where r u guys from ?
@@iknowyouknowleeknow2182 since I also replied, I am from Philippines.
I love that you cover so many different kinds of examples in your videos, not just easy or simple ones. Not too many others are doing that. That tend to want to stick to the basics or keep it simple for us when the problems we are having to solve are more complex than that and require that we understand all the rules - not just the basic ones. THANK YOU!
This is the absolute best math video I have ever seen. It gets straight to the point and not only tells me what I need to know, but teaches it thorough yet concisely.
10/10 IGN
Hours of reading slides, going to lectures and reading textbooks yet it only took your video for this concept to click in my brain. I'm ecstatic. Thanks to you I can get a little bit more sleep tonight :)
This is amazing... I get so frustrated with textbooks that briefly explain one example without covering or explaining "why". You did a great job breaking it down in a way that makes sense. I find that knowing the "why" behind things makes it so much easier to comprehend. Thank you so much for this video!!!!!!!!!!
Thank you for making me say “OHHHHH” 😂😂
This is really helpful now that we're self-studying
Uuuutyqq and pachagura and
I have struggled with this topic for a very very long time.. I cannot even begin to explain how thankful I am.. Thank G-d for you.. You should do video on domain and range for trig functions, that be great..
@Dm Wreath You generally can't find the square root of a negative number. It'll make it complex and we don't want that.
@Dm Wreath you dont need to know why you cant square root a negative. that's when you get a masters or PhD so dont worry
this dude explained everything I need in less than 20 mins, which my professor couldn't in whole semester
good to see people still use these videos too😭
Understood the topic which was supposed to be completed in three weeks, in just 18 minutes. You are really wonderful. Very hard to find such teachers like you.
I feel like I am studying in the “CZcams college “ frr
smallworkz.com
Same
I am studying this in class 10 what about you?
I'm also thinking the same .🤔
Noori 《VLOGS》 why you studying in this pandemic thoo!?
Just started my first year of engineering and after a week of calc. I’m completely lost... came here and this guy is saving lives. Much respect bro, you explanations are clear and concise. Keep those videos coming👍
On g 😭😭
they don't prepare you in high school ehh?
I live in Greece, here we learn all that in high school.
I think in America they call it pre-calculus or something.
@@jesushentaichrist5362 We have calculus as well. AP calculus. Not all people take calculus though, and it sometimes depends on whether it is a private or public school.
@@sdnvdfadsvdfsvard3058 wait.. so in america do you have like separate math classes for different topics?? Like there will be a separate class for trig, pre-calc, calc, algebra etc.?
In Australia we basically have 4 levels when you get to grade 11 and 12:
Standard maths - the easiest you can get. Like basic algebra, trig etc. (Best for people who don't necessarily need much math for their degree and/or job)
Advanced maths - harder algebra, trig, calculus etc. (This level of maths is the lowest needed to get into university for say an engineering, physics, or math degree)
Maths extension 1 - Even harder (Best for people who want to become more math-literate. Will help out more for the degrees listed in advanced math)
Maths extension 2 - The hardest (Same as extension 1. Deeply understanding this course will lead you to acing your university degree.)
I'm curious as to what the 'structure' is in American grade 11 and 12.
@@sdnvdfadsvdfsvard3058 we do this all things in class 11 for jee it is just a piece of cake for a average indian student preparing for jee advanced
I try to understand the domain and range many times but the concept you gave, clear all my doubts . Thanks a lot sir ❤
People who are watching this video fully, are you guys getting that "high" like me? You know, when you finally "get" something and immediately the satisfaction makes you feel so good and suddenly very confident that you'll be able to solve questions like these... oh gosh, my serotonin levels just shot up.
yup
I swear I don't know how i was gonna pass without your help especially with online schooling. I was literally crying for hours today until i stumbled across your video thank you thank you from the bottom of my heart. i think you just gave me hope for passing this course:) please never stop posting.
We personalise teaching on the premise that every human being is uniquely made/created. Every students has intelligence that is unique and different from other students. Similarly learning abilities and styles also vary from student to student. Keeping in view this theory one on one class with student can help student more in learning than a combined class.Moreover, it would be easy for a teacher to assess student by pointing out weakness and work on them to enhance learning and performing best in the exams etc. This can only be made possible if a teacher is certified pedagogist and he/she excelled in subject/course teaching content with enough teaching experience. We offer following course individual tutorial/classes online.
Mathematics: Grade 1-12 (IGCSE/A,O levels), Canada, USA, UK based syllabus
Physics Grade 1-12 (IGCSE A/O levels), Canada, USA, UK based syllabus.
English grammar and composition.
Biology upto grade 8.
Note: We also help students in learning Quran online. Fee is $40/month. Tajweed, hifz, Dua and wazaif, Arabic course and fiqa Hadith.
Fee details:
$5/hr to $20/hr.
Contact: +923018511445:
Skype: join.skype.com/invite/guqjw35byDPE
@@onlineexamshelp9157 why
After watching this video, I feel more confident to face my students.
Why so you are not a good teacher. The teacher these day are so bad
hahaha
boi
jingrags don’t give your kids homework
Min 3 : 20 i didn't understand can you help me how he find (x-4)(x-5)
You're so excellent at explaining things that I have come to deliberately search out your videos specifically on all my university math, physics, and chemistry courses. This content is greatly appreciated and you have a gift for teaching in a way that is easy to understand. Thanks for all you do. I know you are helping a lot of people.
had my first pre-calc assignment last week on this topic. accidentally zoned out in class and had no idea what to do on the homework. but your video helped me understand everything. Thanks!
this helped me a lot. it was clearer and more organized than any other video i have been trying to understand...but couldnt. however, yours did.
You make maths so much more easier, I gave up math at 10th, now in uni... I'm understanding it's not hard, math is easy if you have strong basics....and you are making it happen... thankyou so much ❤️
I've been subscribed for a long time & I just want to say THANK YOU for getting me through my college math courses! The way you explain the math steps & why there might be an invisible number that you have to know sometimes with certain math problems. My college math was following John Squires and it was so difficult to understand certain problems & how he automatically figured it out without explaining step by step. You're literally my teacher & will always be!
I have a test this morning and I won't lie this explanation have taken all my fear n I've done it..all thanks to the organic chemistry tutor ❤️I wish my professor can learn from here just direct and simple no thinking or moving around before getting on track while the students are already confused.thumbs up
this has taught me more than I have ever learned in my precalc class this entire week. thank you!
The first few minutes I knew youre worth the time. You just made my once again encounter with calculus a joyful and thriller of a ride.
MR. Organic Chemistry Tutor, thank you for another fantastic video on How to Find the Domain of a Function. The examples are well explained from start to finish. Drawing a number lined makes the domain easy to find.
I think this is the faceless youtuber who deserves all the attention , not only he assists us in most of our courses but helped many of us ace our exams.
Good, reasonable, intelligent and simple, and pure articulations.
Thank you for such a eloquent manner.
God bless you, my friend
I can say that I am better in math, physics, and chemistry because of this legend. I graduated high school with good grades and now he is helping me in college. THANK YOU SO MUCH LEGEND! I wish you a happy life.
I love the way you explain, you are truly a hero for everybody who is struggling with math, thank you for existing and sharing your knowledge with us, you are amazing!
i just want to let you know you are really saving lives you really explain in a really calm voice and cover all the basics thank you so much
Your explanations ARE AMAZING please keep making videos
Zoey Winston you are amazing
Halo Sedrick ??
I have learned it in my high school but I was like an alien to these things when I came back after three or four years now. even though I remembered things like definitions and other stuff, I wasn't able to apply it anywhere. but now it's lucid in my mind.thank you
Thank you so much for such great help . You just kicked my stress away. I was so stressed about my upcoming test because I didn't understand anything about domains prior to this video. Thank you so much.
God bless you and keep making more videos because they are really helpful
The perfect thing in this video in which it can suit anyone is that his language is easy and he speaks in a clear way thanks!!!!
This helped me so much that I didn’t skip the ads
Besides that this guy is an amazing tutor, his voice is a therapy. Just listening to him doing math problems makes me gain more confidence.
I would just like to say:
During Covid my school opened despite the spread of the virus. I have someone in my family with a comorbidity and so I didn’t go to school. I sat down at home and self studied. And for the first time I had extra maths to study. It looked so tough but your videos were SUPER SUPER helpful. Thank you so much. I passed and got reasonably good marks. You explain so well 😊
Hands down the best teacher I've ever come across. Thank you JG. You're a gift to us all! A God send is perhaps a more accurate description of what you are.
im never skipping ads in this channel. this helped me so much.
Second time taking Calculus. I figured "Oh, I'll just take Summer off from math. Maybe that'll help!" Three hours before class and I realized I forgot just about everything. It's easier learning the second time around. Thank you a ton \o/
Thank god for this video, I had my exam today morning and I quickly pulled up this video right before. NOW I GOT FULL MARKS!!!!!
GOD BLESS YOU!!!!!!!
This guy needs a certified batch for being soo relatable to topic, this guy has made to achieve the toughest part of of past to simplest thing of my life today ✨.
Thanks to The Organic Chemistry Tutor.By this I has been scored some marks in my I.I.T.EXAM.
I really like his voice!
ya he got that latino cholo voice
dog no he doesn’t weirdo
I like u
EASY their mami
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Amazing videos, I have been watching you for my chemistry and math classes and you have helped carry me through them. Thank you!
Am poor in math and i have been struggling during lessons at the campus ,so when i decided to check on you tube i found out that there are helpful video and this really helped me to understand domain and range since i was never taught this in my secondary school.may the almight bless this man 👍👍👍👍
Geez! this has to be the easiest explanation out there... Thank you! exactly what I was looking for
Thanks man, I’m in honors pre calc and still had completely forgotten to find domain and a lot of other stuff since the pandemic. Thanks alot
THANK YOU SO MUCH, this is the first lesson my teacher didnt explain completely. just listening to you for 2 minutes helped me learn more that what my teacher “taught” us in one entire boring class
Thank you for this! I entered college with no calculus background pursuing a calculus-needed program, so I hope I learn a lot in here as I am already learning.
The fact that someone known as the Organic Chemistry Tutor can teach math better than my actual teacher throws my entire educational journey into question.
I cant say how nice video it was as i understood each end everything....thanks
This is a real good lesson just for context. This topic is relevant for so many lessons and it's helping me even in Composition of Functions.
I'm going to have to give you credit when I graduate because my profs have failed me entirely. But you've been a saving grace. It's a kick in the gut that the course I paid hundreds for is taught exceptionally subpar comapred to a guy on CZcams who teaches things effectively. ~20 minute video > 2 hour lecture. Make it make sense. I can't thank you enough for your vids!
Probably one of the most neat and decent explanations I've ever seen. I always struggled with this concept but now, its crystal clear. Thank you for giving such a brief yet explanatory video. And, thank you for not doing a cringe intro and getting straight to the point.👍❤
This video has me seriously questioning the teaching ability of my college professor. So much info in this video was never even mentioned when we went over this section of the chapter!! My study group and I have been so stressed out about our test over this next week because of this and after watching this and sending it to them as well, we finally feel like we've finally learned something!
Thank you so much for this. I'm in Trig and it's been 3 years since my last math class. I am having to re-learn ALL the basics and this helps so much
You are a lifesaver. I failed test at university that was about functions .I got so overwhelmed that I stop and started to write for the sake of finishing. I have been feeling really miserable after writing that test. I am glad I came across this video. You literally saved me from failing again. I hope I pass the next test that will be based on functions and limits. I will come back someday and comment about how my marks have changed for the better. Hopefully.
Damm, that killing voice. This guy just solved my homework actually.
I'm a secondary student and i do take this at school, I speak a different language but i needed to watch this English video because it's shorter than the other ones in my language..i was amazed by the way he explains it! And i think it's alot less complicated and reasonable than the way they explain in my country :/ ...although it's kinda the same way ,but here he makes more sense! It's kinda disappointed to me knowing that there're more better ways to learn Maths (which is my favorite )but it's not available in my education system here so gotta live with it so far :'))
8:28
Anyway ,you know at this part i think that my private teacher's technique is alot easier so I would really like to share it in case anyone needs it (also as a pay back for this amazing explaination)
HERE IT IS:
You determine the signs on each part depending on the "X" 's sign in the equation...
For example as you can see in this equation 8:28, the "X" sign is +POSITIVE so what you're gonna do is use the "LOL" method ..well hold up lemme explain😂
SIMPLY the "LOL" method means: (LIKE, OPPOSITE, LIKE) ...
which means:
LIKE the "X" sign➡️(+)
OPPOSITE the "X" sign➡️(−)
LIKE the "X" sign➡️(+)....
Did you get what i mean? It's gonna be exactly the same answer he said: (+___−___ +)
That's how it works in every equation, as simple as that ,you don't need to do these steps as long as there's an easier way :) ....
And by the way if it's only one "X" solution and not two .. You can still use the same method BUT the whole line will be the same as "X" 's sign in the equation, like if we take it on this equation so then it's all gonna be positive (_+__+_) /(__+__).
That's all what i wanted to say, i know I made a very long comment sorry for that :').... I just hope I helped you a little with this
Oh yeah, our teacher also explained it that way. if "x"s sign is positive, starting from the right it will change from plus to minus (starting with plus) :) and if you see that "x" has negative sign, you can just multiply both sides to -1, but we need to not forget change "" signs too :)
When I teach about number line,my students always have problem about “greater than” or “greater than or equal” sign. Combining to inequality, questions becomes more harder. Combining to inequality graphs, it’s more harder. This videos is not about 1 things in math but also about “something” in student’s head. The numbers views of this video is proof. Thank you so much.
just came here to say that this dude is a real G, helped so many people in my university, i wish him only the best
Thank you, FOR SAVING MY LIFE.
Can you please do a range version of this? it would be really helpful :(
Procrastination Police range is ez. Just input the domains u got in the function, and all the possible results= the range . There’s an Indian woman that explains it .. u should watch that it was rlly helpful
@@The_X25 please give a link if you can :)) thank you
smallworkz.com
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Please do please!!!!!!! 🙏🏽🙏🏽🙏🏽🙏🏽🙏🏽🙏🏽🙏🏽🙏🏽
I completed my homework thanks to you. Had to watch it twice but very nicely explained and covers all exclusivities
I only have a textbook for my online class and seeing you use visuals and explaining the concepts in detail has helped me understand it better, can't thank you enough.
This is why I was so far behind until recently. Textbooks suck. Especially for math
Hats off to u bro. you are a really blessing for me.
my teacher just did a lesson on this and I did not understand a thing. sort of but not really. you're a lifesaver thank you for explaining it so well.
This 18 minutes video was much better than my 1 and half week of my math class. That's sad.
easy and to the point explanation thanks !
We personalise teaching on the premise that every human being is uniquely made/created. Every students has intelligence that is unique and different from other students. Similarly learning abilities and styles also vary from student to student. Keeping in view this theory one on one class with student can help student more in learning than a combined class.Moreover, it would be easy for a teacher to assess student by pointing out weakness and work on them to enhance learning and performing best in the exams etc. This can only be made possible if a teacher is certified pedagogist and he/she excelled in subject/course teaching content with enough teaching experience. We offer following course individual tutorial/classes online.
Mathematics: Grade 1-12 (IGCSE/A,O levels), Canada, USA, UK based syllabus
Physics Grade 1-12 (IGCSE A/O levels), Canada, USA, UK based syllabus.
English grammar and composition.
Biology upto grade 8.
Note: We also help students in learning Quran online. Fee is $40/month. Tajweed, hifz, Dua and wazaif, Arabic course and fiqa Hadith.
Fee details:
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Contact: +923018511445:
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So much respect to u for explaining every single step in detail
This was the best maths CZcams video i have ever watched till now.
Great work man!
Great video,
Very helpful
Thank you:)
here on the night before finals. This really helped me not fail :)
Thank you so much, I was beating my head against a wall. I'm in an online class and the teacher is non-existent pretty much so I'm teaching myself through youtube. It's going well because of people like you. Thanks again!
Thnx a lot dude was struggling while solving those inequalities but now every concepts are cleared.
I will be really grateful to u..
I can't imagine a greater fear on this planet then searching for a subject and seeing that this guy hasn't made a video on it. Absolute legend.
Thanks Sir My respect to you....Also with a salute!❕👍
Finally got a clear picture about domain. You helped me a lot than you think. I owe you!!!
Literally thank you I'm not gonna fail my math class this year because of you my teacher literally only gives us the homework and then tells us the answers the day after he never explains you are teaching more than he has in the past month
why is everyone in the comments a mood and a half? and this guy literally made a video thats less than 20 min long make sense than the whole hour my teacher used up.
dasdasd
We personalise teaching on the premise that every human being is uniquely made/created. Every students has intelligence that is unique and different from other students. Similarly learning abilities and styles also vary from student to student. Keeping in view this theory one on one class with student can help student more in learning than a combined class.Moreover, it would be easy for a teacher to assess student by pointing out weakness and work on them to enhance learning and performing best in the exams etc. This can only be made possible if a teacher is certified pedagogist and he/she excelled in subject/course teaching content with enough teaching experience. We offer following course individual tutorial/classes online.
Mathematics: Grade 1-12 (IGCSE/A,O levels), Canada, USA, UK based syllabus
Physics Grade 1-12 (IGCSE A/O levels), Canada, USA, UK based syllabus.
English grammar and composition.
Biology upto grade 8.
Note: We also help students in learning Quran online. Fee is $40/month. Tajweed, hifz, Dua and wazaif, Arabic course and fiqa Hadith.
Fee details:
$5/hr to $20/hr.
Contact: +923018511445:
Skype: join.skype.com/invite/guqjw35byDPE
So helpful, thank you 😊
ive been trying to understand this for the past 5 months. ive finally got an idea of what to do now. thank you
THANK YOU SO MUCH YOU ARE A LIFE SAVER i have a final exam after 2 days i've been trying to understand this for a long time
Thank you. There aren't many recent CZcams tutors.
Kevon Wallace which country you are from??
true
@@tablafever2077 janede bhai apne category wale nahi hai wo
THANK YOU!! you gave all examples that my college homework included but my instructor did not in his own lecture and notes!!
How do you manage to explain physics, mathematics , biology and chemistry this brilliant.you are God given second Messiah.You have really given me merits in all my courses.
Watching this 4 years later and realizing it got uploaded months after I graduated high school brings me memories, I wish I had something like this when I was doing pre-cal. Brings me tears knowing I had better understanding after watching this video.
sorry its life ,was never meant to be but whereever you are am sure you will make it ,dont be sad
Awesome man! More introductory math videos please! so helpful!