Hey guys, need help with a question
"Give examples of two functions, f(x) and g(x), such that limx→1f(x) does not exist, limx→1g(x) does not exist, but limx→1(f(x)/g(x))=0."
1. a and b are real numbers with $\displaystyle a\ne b\ \wedge\ a\ne 1\ \wedge\ b\ne 1$.
2. Let $\displaystyle f(x)=\dfrac{x+a}{x-1}$ and $\displaystyle g(x)=\dfrac{x+b}{(x-1)^2}$. Then the limits
$\displaystyle \lim_{x \to 1}(f(x))$ and $\displaystyle \lim_{x \to 1}(g(x))$ don't exist.
3. You now can close the existing gap such that the limit $\displaystyle \lim_{x \to 1}\left(\dfrac{f(x)}{g(x)} \right) = 0$