Question 1

Evaluate $$\displaystyle \lim_{x 	o -2^-} f(x)$$ using the graph provided.

Accepted Answer

$$5$$

Question 2

Evaluate $$\displaystyle \lim_{x 	o -2^+} f(x)$$ using the graph provided.

Accepted Answer

$$2$$

Question 3

Which of the following best describes the type of discontinuity at $$x = -2$$ for the function $$f(x)$$ shown in the graph?

Accepted Answer

Jump discontinuity

Question 4

Evaluate $$\displaystyle \lim_{x 	o 3^-} f(x)$$ using the graph provided.

Accepted Answer

$$-\infty$$

Question 5

Evaluate $$\displaystyle \lim_{x 	o 3^+} f(x)$$ using the graph provided.

Accepted Answer

$$\infty$$

Question 6

What is the domain of $$f(x) as $$shown in the graph? (Give your answer in interval notation.)

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 7

Use the Four-Step Procedure to find the derivative of $$f(x) = -3x^2$ + 4x - 2. $$What is $$f'(x)$$?

Accepted Answer

$$-6x + 4$$

Question 8

Find the derivative of $$f(x) = \frac{1}{2}x^3$ - 5x^2$ + 7x - 2.$$

Accepted Answer

$$\frac{3}{2}x^2$ - 10x + 7$$

Question 9

Given $$C(x) = 5000 + 40x + 0.05x^2$, what is the marginal cost when x = 100$ bicycles?

Accepted Answer

$$45$$

Question 10

Given $$C(x) = 5000 + 40x + 0.05x^2$, what is the average cost when x = 100$ bicycles?

Accepted Answer

$$95.5$$

Question 11

Find the derivative of $$f(x) = 3x^2$ e^x.$$

Accepted Answer

$$6x e^x + 3x^2$ e^x$$

Question 12

Find the derivative of $$g(y) = \frac{2y + 5}{3y - 4}.$$

Accepted Answer

$$\frac{6y - 8 - 3(2y+5)}{(3y-4)^2$}$$

Question 13

Find the derivative of $$h(z) = z^3$ \ln(z^2$).$$

Accepted Answer

$$3z^2$$ \$$ln(z^2$$) + $$z^3$$ \cdot \frac{2}{z}$$

Question 14

Which of the following best describes the behavior of $$f(x) as$$ $$x$$ approaches $$3$$ from the left, based on the graph?

Accepted Answer

$$f(x)$$ approaches $$-\infty$$

Question 15

At which $$x-$$value does $$f(x)$$ have a removable discontinuity, based on the graph?

Accepted Answer

$$x = 0$$

Business Calculus Study Guide: Limits, Continuity, Derivatives, and Cost Analysis

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