Homework

Problem 1 · easy

Evaluate lim x->2 (x^2 - 4)/(x - 2).

Problem 2 · medium

Evaluate lim x->0 sin(5x)/x.

Problem 3 · easy

Differentiate f(x) = x^4 - 3x^2 + 5x - 1.

Problem 4 · medium

Differentiate f(x) = x^2 * cos(x).

Problem 5 · medium

Differentiate f(x) = (3x + 1)^6.

Problem 6 · medium

Differentiate f(x) = sin(x)/cos(x).

Problem 7 · easy

Find dy/dx for x^2 + y^2 = 16.

Problem 8 · easy

Find the slope of x^2 + y^2 = 25 at (3, 4).

Problem 9 · medium

Find all local extrema of f(x) = x^3 - 12x.

Problem 10 · medium

Find the absolute minimum of f(x) = x^2 - 6x on [0, 5].

Problem 11 · medium

A ball has v(t) = 10 - 2t. Find the net displacement on [0, 10].

Problem 12 · easy

Find ∫ (x^3 - 2x + 5) dx.

Problem 13 · easy

Find ∫ (6x^5 - 3x^2 + 2) dx.

Problem 14 · easy

Evaluate ∫[0 to 2] (x^2 + 1) dx.

Problem 15 · medium

Evaluate ∫[0 to pi] cos(x) dx.

Problem 16 · medium

Find f(x) given f'(x) = x^2 - x and f(0) = 1.

Problem 17 · medium

Related rates: A circle's radius grows at 5 cm/s. How fast is the area growing when r = 10?

Problem 18 · challenge

Find the x that minimizes f(x) = x^2 + 50/x for x > 0.

Problem 19 · easy

Find d/dx [∫[0 to x] (t^3 + t) dt].

Problem 20 · medium

Evaluate ∫[1 to 3] (x - 1)^2 dx.

Problem 21 · medium

Find the area between y = 4 and y = x^2 on [-2, 2].

Problem 22 · medium

Differentiate f(x) = sqrt(x^2 + 4).

Problem 23 · medium

Linearize f(x) = sqrt(x) at a = 9 and estimate sqrt(9.5).

Problem 24 · challenge

Find all inflection points of f(x) = x^4 - 4x^3.

Problem 25 · challenge

A box with square base (no top) must have volume 32 cm^3. Minimize the surface area. Give the base side length.