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

g) [2] Does the limit of f as $𝑥 \to 2$ 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) $lim_{x \to 4} \frac{x^{2} - 6 x + 8}{x^{2} + x - 20} =$

b) $lim_{x \to 2} \frac{1 - \frac{1}{x - 1}}{x - 2} =$

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

$g (x) = {\begin{cases} \frac{\sqrt{x + 1} - 2}{x - 3} & if x \neq 3 \\ 2 c + 1 & if x = 3 \end{cases}$