1. Limits and Continuity

Find the limit.

$\(\lim\)_{x\(\rarr\)3}\(\frac{x^2+2x-3}{x-2}\)$

Find the limit.

$\(\lim\)_{x\(\rarr\)-\(\pi\)}\(\frac{\sin x}{x}\)$

Find the limit: $\underset{t\to 7}{lim}\frac{7+t^2}{7-t^2}$

Given the function $f\left(x\right)=x$, find the largest value of $\delta$ such that if $|x-4|<\delta |$, then $|x-2|<0.4|$.

Find the limit.

$\(\lim\)_{x\(\rarr\)2}\(\sqrt{x^2+5}\)$

Find the limit.

$\(\lim\)_{x\(\rarr\)0}\(\frac{\sqrt{x+1}\)-1}{x}$

Find the limit.

$\(\lim\)_{x\(\rarr\)0}\(\frac{3x^2+7x}{x}\)$

Find the limit: $\underset{t\to 5}{lim}\frac{5+t^2}{5-t^2}$

Find the limit.

$\(\lim\)_{x\(\rarr\)2}\(\frac{x^2-7x+12}{x-3}\)$

Find the arc length of the graph of the function $y=\frac{2}{3}{x}^{\frac{3}{2}}+\frac{1}{3}$ over the interval $0\le x\le 9$.

Find the limit.

$\(\lim\)_{x\(\rarr\)0}x^3+5x^2-7x+3$

Find the limit.

$\(\lim\)_{x\(\rarr\)3}\(\frac{\sqrt{x}\)-\(\sqrt\)3}{x-3}$