1171 Quiz

14 1171 Quiz

[10 marks total] Use the graph of $𝑦 = 𝑓 ( 𝑥 )$ given below to answer all question on this page.

a) [1] $𝑓 ⁡ ( 3 ) =$	b) [1] $\lim _{x \rightarrow 3} f(x)=$ ${“version”:”1.1″,”math”:”\small \lim _{x \rightarrow 3} f(x)=”}$	c) [1] $\lim _{x \rightarrow-3^{+}} f(x)=$
d) [1] $\lim _{x \rightarrow 0^{+}} f(x)=$ ${“version”:”1.1″,”math”:”\small \lim _{x \rightarrow 0^{+}} f(x)=”}$	e) [1] $\lim _{x \rightarrow 0^{-}} f(x)=$ ${“version”:”1.1″,”math”:”\small \lim _{x \rightarrow 0^{-}} f(x)=”}$	f) [1] $\lim _{x \rightarrow 0} f(x)=$

g) [2] Does the limit of f as $𝑥 → 2$ exist? Support your answer with a statement involving limits.

h) [2] List all x-values on the interval -4 < x < 4 where f(x) has a discontinuity and classify each according to its type.

2. [3 marks each; 6 total] Evaluate the following limits, or state that they do not exist.

a) $\lim _{x \rightarrow 4} \frac{x^{2}-6 x+8}{x^{2}+x-20}=$

b) $\lim _{x \rightarrow 2} \frac{1-\frac{1}{x-1}}{x-2}=$

3. [4 marks] Determine the value of the constant c that will make g(x) continuous at x = 3.

$g(x)=\left\{\begin{array}{ll} \frac{\sqrt{x+1}-2}{x-3} & \text { if } x \neq 3 \\ 2 c+1 & \text { if } x=3 \end{array}\right.$