1. ## Calculus Limit Question

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."

2. Originally Posted by desperatestudent
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 $a\ne b\ \wedge\ a\ne 1\ \wedge\ b\ne 1$.

2. Let $f(x)=\dfrac{x+a}{x-1}$ and $g(x)=\dfrac{x+b}{(x-1)^2}$. Then the limits

$\lim_{x \to 1}(f(x))$ and $\lim_{x \to 1}(g(x))$ don't exist.

3. You now can close the existing gap such that the limit $\lim_{x \to 1}\left(\dfrac{f(x)}{g(x)} \right) = 0$