CALCULUS QUIZ

What is the derivative of the function f(x) = 2x^3?

• 6x^2

• 3x^4

• x^2

• 2x^4

What is the limit of the function f(x) = (x^2 - 1) / (x - 1) as x approaches 1?

• 0

• 1

• Does not exist

• 2

Find the derivative of the function f(x) = sin(x^2).

• 2x * cos(x^2)

• cos(x^2)

• x * cos(x)

• x^2 * cos(x^2)

The derivative of f(x) = 3x^2 - 2x + 5.

The derivative of g(x) = sin(x) + cos(x).

Express sin(2x) in terms of sin(x) and cos(x) using a trigonometric identity.

• sin(x) + cos(x)

• 2 sin(x) cos(x)

• sin^2(x) + cos^2(x)

• sin(x)/cos(x)

Identify the quadrant where cos(x) is positive and sin(x) is negative.

• Quadrant I

• Quadrant II

• Quadrang III

• Quadrant IV

The integral of f(x) = 3x^2 + 2x + 1.

The integral of g(x) = sin(x) + 2cos(x).

A water tank is filled at a rate of r(t) = 5t^2 gallons per minute. What is the expression for the total amount of water W(t) in the tank at time t, given the initial volume W(0) = 100 gallons?

• W(t) = 5t^2 + 100

• W(t) = ∫(5t^2) dt + 100

• W'(t) = 5t^2

• There's not enough information to solve.