Practice Problems

Notice the name of each graphed function. For instance, which function is $C(x)?$

Evaluate the limits$.$ Use clear sentences to explain your reasoning. Eschew pronouns like it and they in favor of clear nouns like function, $x-$values, $y-$values, inputs, outputs.

#$1)$ Evaluate $\underset{x-2}{lim}C(x)$

#$2)$ Evaluate $\underset{x0}{lim}U(x)$

#$3)$ Evaluate $\underset{x-2}{lim}L(x)$

#$4)$ Evaluate $C(6)$

#$5)$ Evaluate $\underset{x2}{lim}U(x)$

#$6)$ Evaluate $L(-2)$

Determine the following limits at infinity. Show clear mathematical reasoning.

#$7)\underset{x4}{lim}[\frac{x+7}{x^4}]$

#$8)\underset{x}{lim}[\frac{x^3+2}{x}]$

#$9)\underset{x}{lim}[\frac{144x^3+1}{12x^3}]$

Complete the proofs below.

#$10)$ Prove $\underset{x2}{lim}(\frac{1}{2}x+2)=3.$ #$11)$ Prove $\underset{x2}{lim}(x^2-1)=3.$ #$12)$ Prove $\underset{x2}{lim}(\frac{3x^3+1}{x^3})=3.$

#$1)-7$

#$3)4$

#$5)0$

$"7)0$

#$9)12$

#$11)$ Use delta$-$epsilon proof