Chapter 5 Quiz 1 Review - Derivatives & Integrals of Natural Log

Find the domain of the function: f(x) = ln(3x+1)

• (-∞, ∞)

• (-1/3, ∞)

• [-1/3, ∞)

• (1/3, ∞)

• None of these.

Find the domain of the function: f(x) = 2 + 1/2 ln(x-3)

• (-∞, ∞)

• (3, ∞)

• [3, ∞)

• (1/3, ∞)

• None of these.

If ln a = 2.565 and ln b = 3.045, find ln(a/b)

• -0.48

• 0.842

• 5.61

• 0.48

• None of these.

If ln a = 2.565 and ln b = 3.045, find 3ln√a

• 3.8475

• 7.695

• 1.2825

• 2.8259

• None of these.

If f(x) = ln (x² + 4x), find f'(x).

• | 2x / x² + 4x | + C

• | (2x + 4) / (x² + 4x) | + C

• | (x² + 4x) / (2x + 4) | + C

• | 2 / (x² + 4x) | + C

• None of these

If f(x) = 2x ln(x²), find f'(x).

• 2 lnx + 2

• 4 lnx + 4

• 2 ln(x²) + 4x

• 4/x

• None of these

Find the second derivative of y = ln (x³√x)

• 7/2x

• -7/2x

• -7/2x²

• 7/2x²

• None of these

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Use logarithmic differentiation to find the derivative: y = (x²√4x+1)/(x³ + 5)³

• 2/x + 2/(4x+1) - 9x²/(x³ + 5)

• 2/x + 1/(4x+1) - 3/(x³ + 5)

• 2/x - 2/(4x+1) - 9x²/(x³ + 5)

• 2/x - 1/(4x+1) - 3/(x³ + 5)

• None of these

Use logarithmic differentiation to find the derivative: y = (x√x² + 2)/√(x³ - 7)

• (x² + 2)/x + 2x²/(x² + 2) + 3x²/2(x³ - 7)

• (x² + 2)/x + 2x²/(x² + 2) - 3x²/2(x³ - 7)

• 1/x + x/(x² + 2) - 3x²/2(x³ - 7)

• 1/x + x/(x² + 2) + 3x²/2(x³ - 7)

• None of these

Evaluate the integral: ∫ (1/x) dx, on the interval (e, 4e).

• ln 3e

• ln 4

• -3/4e

• ln 3

• None of these