007A Sample Midterm 2, Problem 1

Evaluate the following limits.

(a) Find  $\lim _{x\rightarrow 2}{\frac {{\sqrt {x^{2}+12}}-4}{x-2}}$

(b) Find  $\lim _{x\rightarrow 0}{\frac {\sin(3x)}{\sin(7x)}}$

(c) Evaluate  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 0} x^2\cos\bigg(\frac{1}{x}\bigg) }