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aiskarl Group TitleBest ResponseYou've already chosen the best response.0
give 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
 2 years ago

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

REMAINDER Group TitleBest ResponseYou've already chosen the best response.1
let 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 \[ \lim_{x \rightarrow \infty}f(x)+g(x)=1\]
 2 years ago

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

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

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

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

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

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

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