Quiz 4

Date: MATH 1210-4 - Spring 2004

Note: Unless stated otherwise, answers without justification receive no credit. Please, show your work!

1. $\lim_{x\rightarrow 5} \frac{2x^2-11x+5}{x-5} = 9$. Give an $\epsilon$-$\delta$ proof of this fact.

2. Knowing that $\lim_{x\rightarrow 7} f(x) = 1$ and $\lim_{x\rightarrow 7} g(x) = 9$, use properties of the limit operation to find

   $$\lim_{x\rightarrow 7} \frac{2 (g(x)-4f(x))^2}{\sqrt{g(x)}}.$$