Maths Quiz: Calculus

What is the derivative of f(x) = 3x^2 + 2x - 5?

• f'(x) = 6x + 2

• f'(x) = 3x^2 + 2x - 5

• f'(x) = 6x - 2

• f'(x) = 3x^2 + 2

Find the integral of f(x) = 2x + 3 with respect to x.

• The integral of f(x) = 2x + 3 with respect to x is x^3 + 3x^2 + C

• The integral of f(x) = 2x + 3 with respect to x is 4x^2 + 6x + C

• The integral of f(x) = 2x + 3 with respect to x is x^2 + 3x + C, where C is the constant of integration.

• The integral of f(x) = 2x + 3 with respect to x is 2x^2 + 3x + C

What is the limit of (x^2 - 4) / (x - 2) as x approaches 2?

• The limit is 4.

• The limit is 2

• The limit is undefined

• The limit is 0

Solve the differential equation dy/dx = 2x.

• y = x^2 + C

• y = 3x^2 + C

• y = x^3 + C

• y = 2x^2

Find the area under the curve y = x^2 + 3x + 2 from x = 1 to x = 4.

• The area under the curve y = x^2 + 3x + 2 from x = 1 to x = 4 is 45.33 square units

• The area under the curve y = x^2 + 3x + 2 from x = 1 to x = 4 is 10.33 square units

• The area under the curve y = x^2 + 3x + 2 from x = 1 to x = 4 is 20.33 square units

• The area under the curve y = x^2 + 3x + 2 from x = 1 to x = 4 is 39.33 square units

What is the second derivative of f(x) = 4x^3 - 2x^2 + 5x - 1?

• f''(x) = 16x^2 - 3x + 4

• f''(x) = 24x - 4

• f''(x) = 8x^2 - 2x + 5

• f''(x) = 12x^2 - 4x + 5

Evaluate the definite integral of f(x) = 3x^2 - 2x + 1 from x = 0 to x = 2.

• 5.5

• 10.25

• 3.75

• 7.33

Find the slope of the tangent line to the curve y = 2x^2 - 3x + 1 at the point (2, 3).

• 7

• 10

• 5

• 2

What is the value of the limit lim(x->3) (x^2 - 9) / (x - 3)?

• 9

• 0

• 6

• 3

Solve the differential equation dy/dx = 3x^2 - 6x + 2.

• y = 3x^2 - 6x + C

• y = x^3 - 3x^2 + 2x + C

• y = 3x^3 - 6x^2 + 2x + C

• y = x^3 - 3x^2 + 2x - C