009A Sample Midterm 3, Problem 1

Find the following limits:

(a) If  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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