Question 1

Given the graph in Image 1, what is $\displaystyle \lim_{x 	o 4^-} f(x)$?

Accepted Answer

$4$

Question 2

Given the graph in Image 1, what is $\displaystyle \lim_{x 	o 4^+} f(x)$?

Accepted Answer

$6$

Question 3

Given the graph in Image 1, what is $\displaystyle \lim_{x 	o 4} f(x)$?

Accepted Answer

Does not exist

Question 4

Given the graph in Image 1, what is $\displaystyle \lim_{x 	o 9} f(x)$?

Accepted Answer

$-\infty$

Question 5

Given the graph in Image 1, what is $\displaystyle \lim_{x 	o -\infty} f(x)$?

Accepted Answer

$\infty$

Question 6

Given the graph in Image 1, what is $\displaystyle \lim_{x 	o \infty} f(x)$?

Accepted Answer

$6$

Question 7

Given the graph in Image 2, what type of discontinuity is present at $x=0$?

Accepted Answer

Infinite discontinuity

Question 8

Given the graph in Image 2, what is $\displaystyle \lim_{x 	o 0^-} f(x)$?

Accepted Answer

$0$

Question 9

Given the graph in Image 2, what is $\displaystyle \lim_{x 	o 0^+} f(x)$?

Accepted Answer

$0$

Question 10

Given the graph in Image 3, which shows a tangent line at $x=6$, estimate the value of $f'(6)$.

Accepted Answer

$\frac{1}{4}$

Question 11

Given the graph in Image 2, what can you say about the differentiability of $f(x)$ at $x=0$?

Accepted Answer

The function is not differentiable at $x=0$

Question 12

Suppose the graph in Image 1 represents the position of a car over time. What does the limit $\displaystyle \lim_{x 	o 9} f(x) = -\infty$ represent in this context?

Accepted Answer

The car's position drops rapidly downward as time approaches 9

Question 13

Given the graph in Image 1, which of the following best describes the behavior of $f(x)$ as $x$ approaches $9$ from the left?

Accepted Answer

$f(x)$ decreases without bound

Question 14

Given the graph in Image 1, what is the value of $f(4)$?

Accepted Answer

There is a hole at $x=4$, so $f(4)$ is undefined

Question 15

Given the graph in Image 1, what is the value of $f(6)$?

Accepted Answer

$5$

Question 16

Given the graph in Image 1, what is the value of $f(9)$?

Accepted Answer

Undefined

Calculus Exam I Review: Limits and Derivatives – Step-by-Step Guidance

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