A differential equation is an equation involving a function and one or more of its derivatives. Determine whether the function y=πsinθ+2πcosθ is a solution to the differential equation d^2y/dθ^2...

A piece of plexiglass is in the shape of a semicircle with radius 2 m. Determine the dimensions of the rectangle with the greatest area that can be cut from the piece of plexiglass.

Air is being pumped into a spherical balloon. The volume, V, in cubic centimetres, of the balloon is V=4/3πr^3, where the radius, r, is in centimetres.
a) Determine the...

1. Find the derivative f'(x).
(a) f(x)=xexcosx
(b) f(x)=secxtanx
(c) f(x)=sinx/1+cosx
2. Let g(x) be a differentiable function such that g(0)=2 and g'(0)=3.
(a)...

Differentiation - Taking the Derivative
Differentiation is the algebraic method of finding the derivative for a
function at any point. The derivative is a concept that is at the root of
calculus. There are two ways of introducing this concept, the geometrical way (as the slope of a curve), and the physical way (as a rate of change). The slope of a curve translates to the rate of...
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Derivative Proofs
Though there are many different ways to prove the rules for finding a
derivative, the most common way to set up a proof of these rules is to go back to the
limit definition. This way, we can see how the limit definition works for various
functions.
We must remember that mathematics is a succession. It builds on itself, so many proofs rely on results...
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