Linear Approximation, Differentials, Tangent Line, Linearization, f(x), dy, dx - Calculus
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- čas přidán 19. 10. 2016
- This calculus video shows you how to find the linear approximation L(x) of a function f(x) at some point a. The linearization of f(x) is the tangent line function at f(a).
Derivatives - Fast Review: • Calculus 1 - Derivatives
Introduction to Related Rates:
• Introduction to Relate...
Local Maximum & Minimum:
• Finding Local Maximum ...
Mean Value Theorem:
• Mean Value Theorem
Concavity & Inflection Points:
• Concavity, Inflection ...
________________________________
L'Hopital's Rule:
• L'hopital's rule
Curve Sketching With Derivatives:
• Curve Sketching - Grap...
Newton's Method:
• Newton's Method
Optimization Problems:
• Optimization Problems ...
Marginal Cost & Total Average Cost:
• Marginal Cost and Aver...
__________________________________
Marginal Revenue and Profit:
• Marginal Cost, Margina...
Tangent Line Approximations:
• Finding The Linearizat...
Differentials & Local Linearization:
• Differentials and Deri...
Estimating Function Values:
• Estimating Function Va...
Antiderivatives:
• Antiderivatives
__________________________________
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections
Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
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4:18 Find the linearization L(x) of the function a. Use it to estimate f(37) f(x) = x^(1/2) a = 36
8:15 Find the linearization L(x) of the function a. Use it to estimate f(2.1) f(x) = x^(1/3) a = 2
12:10 Estimate the given number using a local linear approximation 8^(1/3)
20:54 Use linearization to approximate ln(1.05)
23:59 Use linearization to approximate tan(46)
30:24 Differentials
36:05 Find the differential of the function y = x^(6) = 7x^(2) +3x
37:35 Find the differential of the function y = x^(2) ln(x)
39:09 Find the differential of the function V = (4/3)πR^(3)
40:36 Find the differential dy and evaluate it using the following values of x and dx
47:56 Graphical representation of differentials
51:11 y = x^(3)-5x+1 and x =2 Δx = 0.1 find dy, Δy
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A key take away from this video is Delta X and Y Vs Dx and Dy. From what I understood the deltas are changes in X and Y values of the Function where Dx and Dy are changes in X and Y of tangent line. My professor probably explained this but I did not grasp it until I watched this video.
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For the tangent function, you’d still need to use an approximation for pi/90. Could you do a video where you use the Taylor approximation theorem to approximate pi/90 and various other transcendental expressions.
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I was a little bit confused about the tan(46) problem, why did you switch from 46 to a radiant, and where did the answer 3 go? so if the 3 is not close to 1.03553, you have to use radiant to get the accurate approximation? Do we have to do that with every problem?
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This is probably never going to get answered, but at 22:00 , why is the deriv of ln(1) = to one? I get the 1/x > 1/1 thing, but also when you consider d/dx lnU = U'/U, then ln(1) = 0 bc it's 0/1.
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How did you know to set f(x) to sqrt x for the first one. And f(x) = x^3 for the second one?
what are the conditions on picking what the a is?
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Thank you