1. limits

Suppose that neither lim x->a f(x) nor limit g(x) exists. Find functions f and g so that the following limits exist or explain why it is impossible to do so.

(a) lim x->a (f(x)+f(x))

(b)lim x->a (f(x) * g(x))

where do I evaluate from?

2. Originally Posted by asweet1
Suppose that neither lim x->a f(x) nor limit g(x) exists. Find functions f and g so that the following limits exist or explain why it is impossible to do so.

(a) lim x->a (f(x)+f(x))

$\displaystyle \color{red}\mbox{I suppose you meant to write here }\lim_{x\rightarrow a}\left(f(x)+g(x)\right)\,,\,\,\mbox{so you can take }$ $\displaystyle \color{red}f(x)=\frac{1}{x}\,\mbox{ and }\,\,g(x)=-\frac{1}{x}\,,\,\,a=0$

(b)lim x->a (f(x) * g(x))

$\displaystyle \color{red}\mbox{Take }f(x)=\left\{\begin{array}{cc}0&\mbox{ if }\,x\leq 0\\1&\mbox{ if } x>0\end{array}\right. \,\mbox{ and }\,\,g(x)=\left\{\begin{array}{cc}1&\mbox{ if }\,x\leq 0\\0&\mbox{ if } x>0\end{array}\right.$

$\displaystyle \color{blue}Tonio$

where do I evaluate from?
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