Homework

Problem 1 · easy

Find the linearization of f(x) = x^2 at a = 3.

Problem 2 · easy

Find the linearization of f(x) = sqrt(x) at a = 9.

Problem 3 · easy

Use linearization of f(x) = sqrt(x) at a = 25 to estimate sqrt(26).

Problem 4 · medium

Use linearization of f(x) = x^(1/3) at a = 8 to estimate the cube root of 9.

Problem 5 · easy

Find dy for f(x) = x^3 when x = 2, dx = 0.1.

Problem 6 · easy

Find dy for f(x) = sin(x) when x = 0, dx = 0.05.

Problem 7 · medium

A circle has radius 8 cm ± 0.2 cm. Estimate the error in area.

Problem 8 · medium

A sphere has radius 5 cm ± 0.1 cm. Estimate the relative error in volume.

Problem 9 · easy

Estimate (0.99)^5 using linearization of f(x)=x^5 at a=1.

Problem 10 · easy

Estimate sin(0.1) using the linearization of sin(x) at a=0.

Problem 11 · easy

Estimate cos(0.05) using linearization of cos(x) at a=0.

Problem 12 · medium

Find dy for f(x) = 3x^2 + x when dx = 0.01 at x = 4.

Problem 13 · medium

Find the linearization of f(x) = 1/x at a = 2.

Problem 14 · medium

Use the linearization of 1/x at a=2 to estimate 1/2.1.

Problem 15 · easy

Find the linearization of f(x) = tan(x) at a = 0.

Problem 16 · medium

If the radius of a cylinder (fixed height h=10) has error dr=0.05 at r=4, estimate the error in volume.

Problem 17 · easy

Estimate sqrt(4.2) using the linearization of sqrt(x) at a=4.

Problem 18 · medium

Find dy for y = cos(x) at x = pi/2, dx = 0.02.

Problem 19 · medium

The relative error in r is 2%. What is the relative error in r^3?

Problem 20 · medium

Use linearization to estimate (8.01)^(1/3) given f(x)=x^(1/3) at a=8.

Problem 21 · medium

Find the linearization of f(x) = ln(x) at a = 1. (Use d/dx[ln x] = 1/x.)

Problem 22 · easy

Use the linearization of ln(x) at a=1 to estimate ln(1.05).

Problem 23 · easy

A square's side is measured at 10 cm ± 0.3 cm. Estimate the error in the area.

Problem 24 · medium

Find the linearization of f(x) = x^4 at a = 2.

Problem 25 · medium

Estimate (1.98)^4 using linearization at a=2.