Quiz about Calculus Mastery Quiz

Question 1

What is the derivative of $$f(x) = x^3$$ ?

Accepted Answer

$$3x^2$$

Answer

$$x^2$$

Answer

$$3x$$

Answer

$$6x$$

Question 2

Evaluate the integral $$\int 3x^2 dx$$ .

Accepted Answer

$$\frac{3x^3}{3} + C$$

Answer

$$x^3 + C$$

Answer

$$x^2 + C$$

Answer

$$\frac{x^3}{3} + C$$

Question 3

What is the limit of $$\frac{x^2 - 1}{x - 1}$$ as $$x$$ approaches 1?

Accepted Answer

2

Answer

0

Answer

1

Answer

Does not exist

Question 4

If $$f$$ , what is $$f(x)$$ ?

Accepted Answer

$$3x^2 + C$$

Answer

$$6x^2 + C$$

Answer

$$x^3 + C$$

Answer

$$2x^3 + C$$

Question 5

What is the second derivative of $$f(x) = 4x^3 - 2x^2 + x$$ ?

Accepted Answer

$$24x - 4$$

Answer

$$12x - 2$$

Answer

$$12x^2 - 4x + 1$$

Answer

$$24x^2 - 4$$

Question 6

Evaluate the definite integral $$\int_{0}^{2} (3x^2 + 2x) dx$$ .

Accepted Answer

$$16$$

Answer

$$12$$

Answer

$$14$$

Answer

$$18$$

Question 7

What is the derivative of $$f(x) = \frac{1}{x}$$ ?

Accepted Answer

$$-\frac{1}{x^2}$$

Answer

$$\frac{1}{x^2}$$

Answer

$$-\frac{1}{2x}$$

Answer

$$\frac{1}{2x^2}$$

Question 8

Find the antiderivative of $$f(x) = e^x$$ .

Accepted Answer

$$e^x + C$$

Answer

$$xe^x + C$$

Answer

$$\frac{e^x}{x} + C$$

Answer

$$e^{x^2} + C$$

Question 9

What is the derivative of $$f(x) = \ln(x)$$ ?

Accepted Answer

$$\frac{1}{x}$$

Answer

$$x\ln(x) - x$$

Answer

$$\ln(x) + 1$$

Answer

$$x\ln(x)$$

Question 10

If $$F(x) = \int_{a}^{x} t^2 dt$$ , what is $$F$$ ?

Accepted Answer

$$x^2$$

Answer

$$2x$$

Answer

$$a^2$$

Answer

$$2a$$

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