009A Sample Midterm 3, Problem 1

Find the following limits:

(a) If  $\lim _{x\rightarrow 3}{\bigg (}{\frac {f(x)}{2x}}+1{\bigg )}=2,$  find  $\lim _{x\rightarrow 3}f(x).$

(b) Find  $\lim _{x\rightarrow 0}{\frac {\tan(4x)}{\sin(6x)}}.$

(c) Evaluate  $\lim _{x\rightarrow \infty }{\frac {-2x^{3}-2x+3}{3x^{3}+3x^{2}-3}}.$

---

Solution

Detailed Solution

Return to Sample Exam