## anonymous 3 years ago give an example

1. anonymous

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. experimentX

try this $\lim_{x \to 0}{\sin^2x x \over x^2}$ expand sin^2 x as 1 + cos^2x

3. anonymous

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 $\lim_{x \rightarrow \infty}f(x)+g(x)=-1$

4. experimentX

try something like of this form where you can take LCM and use L'Hopital's rule $\infty - \infty$

5. experimentX

@REMAINDER 's example is also good example.

6. experimentX

Woops!! $\lim_{x \to 0}{\sin^2x \over x^2} = \lim_{x \to 0}{1 \over x^2}+\lim_{x \to 0}{\cos^2 x \over x^2}$

7. anonymous

???

8. experimentX

both 1/x^2 and cos^2x/x^2 does not exist but the sum exists

9. anonymous

how to know exist or not

10. experimentX

try finding them individually ...

11. experimentX