### Subsection1.3.2Exercises

###### 1

Given the function shown below, evaluate the following:

1. $\displaystyle \lim_{x \rightarrow -2} f(x)$
2. $\displaystyle \lim_{x \rightarrow 0}f(x)$
3. $\displaystyle \lim_{x \rightarrow 2}f(x)$
###### 2

Given the function shown below, evaluate $\displaystyle \lim_{x \rightarrow 0} f(x)\text{.}$

###### 3

Given the function shown below, evaluate:

1. $\displaystyle \lim_{x \rightarrow -1^{-}} f(x)$
2. $\displaystyle \lim_{x \rightarrow -1^{+}} f(x)$
3. $\displaystyle \lim_{x \rightarrow -1} f(x)$
4. $\displaystyle \lim_{x \rightarrow -2^{+}} f(x)$
5. $\displaystyle \lim_{x \rightarrow 2^{-}} f(x)$
###### 4

Draw a curve $y=f(x)$ with $\displaystyle\lim_{x \rightarrow 3}f(x)=f(3)=10\text{.}$

###### 5

Draw a curve $y=f(x)$ with $\displaystyle\lim_{x \rightarrow 3}f(x)=10$ and $f(3)=0\text{.}$

###### 6

Suppose $\displaystyle\lim_{x \rightarrow 3} f(x)=10\text{.}$ True or false: $f(3)=10\text{.}$

###### 7

Suppose $f(3)=10\text{.}$ True or false: $\displaystyle\lim_{x \rightarrow 3} f(x)=10\text{.}$

###### 8

Suppose $f(x)$ is a function defined on all real numbers, and $\displaystyle\lim_{x \rightarrow -2} f(x)=16\text{.}$ What is $\displaystyle\lim_{x \rightarrow -2^-} f(x)\text{?}$

###### 9

Suppose $f(x)$ is a function defined on all real numbers, and $\displaystyle\lim_{x \rightarrow -2^-} f(x)=16\text{.}$ What is $\displaystyle\lim_{x \rightarrow -2} f(x)\text{?}$

###### Exercises — Stage 2

In Questions 1.3.2.10 through 1.3.2.17, evaluate the given limits. If you aren't sure where to begin, it's nice to start by drawing the function.

###### 10

$\displaystyle\lim_{t \rightarrow 0} \sin t$

###### 11

$\displaystyle\lim_{x \rightarrow 0^+} \log x$

###### 12

$\displaystyle\lim_{y \rightarrow 3} y^2$

###### 13

$\displaystyle\lim_{x \rightarrow 0^-} \dfrac{1}{x}$

###### 14

$\displaystyle\lim_{x \rightarrow 0} \dfrac{1}{x}$

###### 15

$\displaystyle\lim_{x \rightarrow 0} \dfrac{1}{x^2}$

###### 16

$\displaystyle\lim_{x \rightarrow 3} \dfrac{1}{10}$

###### 17

$\displaystyle\lim_{x \rightarrow 3} f(x)\text{,}$ where $f(x)=\left\{ \begin{array}{ll} \sin x&x\leq 2.9\\ x^2&x \gt 2.9 \end{array} \right.\text{.}$