Calculus Quiz

Evaluate the integral: ∫ (x³ - 3x) dx =

• 3x² - 3 + C

• 4x⁴ - 6x² + C

• x⁴/3 - 3x² + C

• x⁴/4 - 3x + C

• x⁴/4 - 3x²/2 + C

If f(x) = x³ + 3x² + 4x + 5 and g(x) = 5, then g(f(x)) =

• 5x² + 15x + 25

• 5x³ + 15x² + 20x + 25

• 1125

• 225

• 5

The slope of the line tangent to the graph of y = ln(x²) at x = e² is

• 1/e²

• 2/e²

• 4/e²

• 1/e⁴

• 4/e⁴

If f(x) = x + sin x, then f'(x) =

• 1 + cos x

• 1 - cos x

• cos x

• sin x - x cos x

• sin x + x cos x

If f(x) = eˣ, which of the following lines is an asymptote to the graph of f?

• y = 0

• x = 0

• y = x

• y = -x

• y = 1

If f(x) = (x - 1)/(x + 1) for all x ≠ -1, then f '(1) =

• -1

• -1/2

• 0

• 1/2

• 1

Which of the following equations has a graph that is symmetric with respect to the origin?

• y = (x+1)/x

• y = -x⁵ + 3x

• y = x⁴ - 2x² + 6

• y = (x-1)³ + 1

• y = (x² + 1)² - 1

A particle moves in a straight line with velocity v(t) = t². How far does the particle move between times t = 1 and t = 2?

• 1/3

• 7/3

• 3

• 7

• 8

If y = cos² (3x), then dy/dx =

• -6sin(3x)cos(3x)

• -2cos(3x)

• 2cos(3x)

• 6cos(3x)

• 2sin(3x)cos(3x)

The derivative of f(x) = x⁴/3 - x⁵/5 attains its maximum value at x =

• -1

• 0

• 1

• 4/3

• 5/3