Calculus

Calculus studies how things change. What could be more important than that?

Inverse function theorem to prove f maps open sets to open sets.

4 1/7-2 5/6

√2 * √32

The graph of g(x) is given. • g(x) has horizontal tangents at x = −5, x = −1.1, and x = 4. • g(x) has inflections points at x = −3.1, x = 1, and x = 4. • g(x) has zeros at x = −6.1, x = −3.1, ...

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A balls rolls down a long inclined plane so that its distance s from its starting point after t seconds is S=4,5t²+2t feet. When will instantenous velocity be 30 feet per second?

Find the general solution of the system of ODEs dx dt = −x − y + z dy dt = x − 3y − z dz dt = 2x − 2y − 2z. and write down fundamental matrix Ψ(t) of this system, satisfying the initial ...

A rectangle with length l and width w has a diagonal of D inches. If the perimeter of the rectangle is 80 inches, express the diagonal of the rectangle in terms of w. Use a lower case w.

The Volume of a cube increases at a constant rate of 10 cm^3 per second. find the rate of change in its total surface area at the instant when its sides are 20 cm long.

How do we solve the question below?

two small towns alpha and beta are on opposite of a main road.