Calculus Challenge

What is the derivative of x^2?

• 3x

• 2x

• x^2

• x^3

What is the integral of 3x^2?

• 9x^2 + C

• x^3 + C

• 6x + C

• 3x^3 + C

Find the limit of (x^2 - 1) / (x - 1) as x approaches 1.

• 2

• 0

• 3

• 4

What is the second derivative of sin(x)?

• tan(x)

• cos(x)

• cot(x)

• -sin(x)

Solve the differential equation dy/dx = 2x.

• y = 3x

• y = 2x^2

• y = x^3

• y = x^2 + C

What is the area under the curve y = x^2 from x=0 to x=2?

• 10

• 8/3

• 6

• 4

Find the critical points of the function f(x) = x^3 - 3x^2 + 2.

• The critical points are x = 0 and x = 2.

• The critical points are x = -1 and x = 3.

• The critical points are x = -2 and x = 5.

• The critical points are x = 1 and x = 4.

Evaluate the definite integral of 2x from 0 to 4.

• 16

• 12

• 8

• 20

What is the slope of the tangent line to the curve y = 2x^2 at the point (1, 2)?

• 1

• 3

• 5

• 4

Solve the equation 3x + 5 = 2x - 3.

• x = 5

• x = -8

• x = -2

• x = 0