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aiskarl
 2 years ago
Best ResponseYou've already chosen the best response.0give an example to show that \[\lim_{x \rightarrow a} f(x)\] and \[\lim_{x \rightarrow a} g(x)\] doesnot exist but \[\lim_{x \rightarrow a} (f(x)+g(x))\] exist

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1try this \[ \lim_{x \to 0}{\sin^2x x \over x^2}\] expand sin^2 x as 1 + cos^2x

REMAINDER
 2 years ago
Best ResponseYou've already chosen the best response.1let f(x)=x and g(x)=(x+1) and a=infinity then \[\lim_{x \rightarrow \infty } f(x)=\infty \] and \[ \lim_{x \rightarrow \infty } g(x)=\infty\] but \[ \lim_{x \rightarrow \infty}f(x)+g(x)=1\]

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1try something like of this form where you can take LCM and use L'Hopital's rule \[ \infty  \infty \]

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1@REMAINDER 's example is also good example.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1Woops!! \[ \lim_{x \to 0}{\sin^2x \over x^2} = \lim_{x \to 0}{1 \over x^2}+\lim_{x \to 0}{\cos^2 x \over x^2}\]

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1both 1/x^2 and cos^2x/x^2 does not exist but the sum exists

aiskarl
 2 years ago
Best ResponseYou've already chosen the best response.0how to know exist or not

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1try finding them individually ...

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1http://www.wolframalpha.com/input/?i=lim+x%3E0+cos^2x%2Fx^2
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