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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