How to Find Limits by Conjugate Method (Rationalizing)

How to find limits by conjugate method, or rationalizing? In this video, we will discover how to apply the conjugate or rationalizing method in finding the limits for a function. We will also discuss when we should use the conjugate, or rationalizing method.
We use the conjugate method, or known as rationalizing, when direct substitution fails. Direct substitution fails when we plug the value of x into the limit and ends up with zero divided by zero, which is one of the indeterminate forms. Therefore, we need to multiply by the conjugate for rationalizing.
#calculus #limits #conjugatemethod
TIMECODES:
0:00 Example 1
2:16 Example 2
3:42 Self-Exercise

[@jan-willemreens9010]

... The 2nd indeterminate limit can also be solved as follows ... in this case rewriting the numerator x - 5 as (4 + x) - 9 , and considering this expression as a difference of 2 squares ... (4+ x) - 9 = (SQRT(4 + x) - 3)(SQRT(4 + x) + 3) ... then cancelling common factor SQRT(4 + x) - 3 between top and bottom, giving us a solvable limit form in return ... lim(x->5)[SQRT(4 + x) + 3] = 6 ... solving this limit by factoring and cancelling ... thank you for your clear and instructive presentations ... take good care, Jan-W

[@jan-willemreens9010]

... Good day to you, Another way of solving your indeterminate limit, is to rewrite the denominator x in its original form as follows ... x = (4 + x) - 4 , and then treating this expression as a difference of 2 squares ... (SQRT(4 + x) - 2)(SQRT(4 + x) + 2) to finally cancelling the common factor (SQRT(4 + x) - 2) between numerator and denominator, to be left with a solvable limit form ... lim(x->0)[1/(SQRT(4 + x) + 2) = 1/4 ... solving by factoring I think I would call this ... thanks for sharing your instructive math channel with us, the interested viewers ... best wishes, Jan-W

[@raznologija745]

Excellent explanation

[@YeahMathIsBoring]

Thanks!

[@rkstudying]

please make more videos on integration

[@rkstudying]

1/2 is it right?

[@Nifaofficial-ic9db]

Anyway thnkx so I got problem why u conjugate numerator instead of conjugating denominator x

[@YeahMathIsBoring]

It depends on situations. We actually want to get rid of the square root, so we multiply the fraction by the conjugate of the expression that has a square root. For example, if the square root is in the numerator, we multiply it by the conjugate of numerator instead of denominator.