Calculus

This section explores some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velocity in physics, population growth rates in biology, and marginal...

Given a function f(x) where f(x) ≥ 0 over the interval a ≤ x ≤ b, we investigate the area of the region Given a function f(x) where f(x) ≥ 0 over the interval a ≤ x ≤ b, we investigate the area of the region that is under the graph of f(x) and above the interval [a,b]...

Antiderivatives The reverse process of the derivative or a differential is called antidifferentiation.  The steps of finding an antiderivative   Integrals This section explores integrals involving trigonometric functions and some of the techniques we can use...

We begin our exploration of the derivative for the sine function by using the formula to make a reasonable guess at its derivative. Recall that for a function f(x), By setting D(x)= ( sin⁡(x+0.01)–sin⁡x) ÷ 0.01 and using a graphing utility, we can get a graph of an...

We have seen that as we travel around the unit circle, the values of the trigonometric functions repeat. We can see this pattern in the graphs of the functions. Let P = (x,y) be a point on the unit circle and let θ be the corresponding angle. Since the angle θ and...