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cinar
 2 years ago
Best ResponseYou've already chosen the best response.0\[\LARGE \lim_{x \rightarrow a}\frac{x^\sqrt{2}a^\sqrt{2}}{xa}\]

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0I would consider rationalizing the numerator AND denominator first.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0Never mind. Factor the numerator.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0@cinar: If that was your answer you are incorrect. I should mention.

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0the answer is \[\sqrt{2}a^{\sqrt{2}1}\]if L'Hospital rule is allowed, but without using it, I have no idea..

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1This is the (less often seen) version of the Limit Definition of a Derivative,\[\large f'(x)=\lim_{x \rightarrow a}\frac{f(x)f(a)}{xa}\]So identity f(x), then just take it's derivative.

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0I am not looking for derivative of it, it is limit question..

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1This limit represents the LIMIT DEFINITION OF A DERIVATIVE. You are not actually expected to evaluate the limit. You're suppose to recognize that it represents a derivative.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Example: Evaluate the limit:\[\large \lim_{h \rightarrow 0}\frac{(x+h)^2x^2}{h}\] You could do the work simplifying it down, Or you can recognize that this is the DERIVATIVE of\[\large f(x)=x^2\]

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0\[ f'(x)=\frac{a^{\sqrt2}+\sqrt2 x^{\sqrt21} (xa)x^{\sqrt2}}{(ax)^2}\]

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1\[\large f'(\color{red}{a})=\lim_{x \rightarrow a}\frac{f(x)f(a)}{xa}\]Ah sorry I made a small typo,

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0but we cannot simplify it can we?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1So that's where the a in coming from in the answer i guess :D

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1You just need to recognize that,\[\large f(x)=x^{\sqrt2}\]And that this limit represents,\[\large f'(a)\] So simply take the derivative of f(x), then plug in a! :)

cinar
 2 years ago
Best ResponseYou've already chosen the best response.0\[\large \lim_{h \rightarrow 0}\frac{(x+h)^2x^2}{h}=2x ?\]
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