Calculus

A circle's radius is increasing at 3 cm/s. How fast is its area increasing when the radius is 5 cm?

A rectangle has a perimeter of 40 meters. Find the dimensions that maximize its area.

Evaluate the definite integral ∫ from 0 to 2 of (3x^2 + 1) dx.

Evaluate the limit: lim(x→0) (sin x)/x.

Evaluate the limit: lim(x→3) (x^2 - 9)/(x - 3).

Find the derivative of f(x) = 4x^3 - 5x^2 + 7x - 9.

Find the derivative of f(x) = (x^2 + 1)(3x - 4).

Find the equation of the tangent line to f(x) = x^2 + 2x at x = 1.

Find the indefinite integral ∫(6x^2 - 4x + 5) dx.

Let F(x) = ∫ from 1 to x of (t^2 + 4t) dt. Find F'(x).