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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
 one year 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
 one year 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 \[ \lim_{x \rightarrow \infty}f(x)+g(x)=1\]
 one year 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 \[ \infty  \infty \]
 one year ago

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

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

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

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