14 1171 Quiz
Math 1171 Quiz
- [10 marks total] Use the graph of [latex]𝑦 = 𝑓 ( 𝑥 )[/latex] given below to answer all question on this page.
| a) [1] [latex]𝑓 ( 3 ) =[/latex] | b) [1] [latex]\lim _{x \rightarrow 3} f(x)=[/latex] | c) [1] [latex]\lim _{x \rightarrow-3^{+}} f(x)=[/latex] |
| d) [1] [latex]\lim _{x \rightarrow 0^{+}} f(x)=[/latex] | e) [1] [latex]\lim _{x \rightarrow 0^{-}} f(x)=[/latex] | f) [1] [latex]\lim _{x \rightarrow 0} f(x)=[/latex] |
g) [2] Does the limit of f as [latex]𝑥 → 2[/latex] 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) [latex]\lim _{x \rightarrow 4} \frac{x^{2}-6 x+8}{x^{2}+x-20}=[/latex]
b) [latex]\lim _{x \rightarrow 2} \frac{1-\frac{1}{x-1}}{x-2}=[/latex]
3. [4 marks] Determine the value of the constant c that will make g(x) continuous at x = 3.
[latex]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.[/latex]