Questions from General Calculus

Q: Find constants A and B such that the function y = A

Find constants A and B such that the function y = A sin x + B cos x satisfies the differential equation y" + y' – 2y = sin y.

Q: The function f (x) = sin (x + sin

The function f (x) = sin (x + sin 2x), 0 < x < π, arises in applications to frequency modulation (FM) synthesis. (a). Use a graph of f produced by a graphing device to make a rough sketch of the graph...

Q: The figure shows a circular arc of length s and a chord

The figure shows a circular arc of length s and a chord of length d, both subtended by a central angle θ. Find

Q: Assume that a snowball melts so that its volume decreases at a

Assume that a snowball melts so that its volume decreases at a rate proportional to its surface area. If it takes three hours for the snowball to decrease to half its original volume, how much longer...

Q: (a). Use a graphing calculator or computer to graph the

(a). Use a graphing calculator or computer to graph the function f (x) = x4 – 3x2 – 6x2 + 7x + 30 in the viewing rectangle [-3, 5] by [-10, 50]. (b). Using the graph in part (a) to estimate slopes, ma...

Q: Where is the greatest integer function f (x) = [[

Where is the greatest integer function f (x) = [[x]] not differentiable? Find a formula for f' and sketch its graph.

Q: Where does the normal line to the parabola y = x –

Where does the normal line to the parabola y = x – x2 at the point (1, 0) intersect the parabola a second time? Illustrate with a sketch.

Q: Let f (x) = x3 - x. In Examples

Let f (x) = x3 - x. In Examples 3 and 7 in Section 2.7, we showed that f'(x) = 3x2 - 1 and f"(x) = 6x. Use these facts to find the following. (a). The intervals on which f is increasing or decreasing....

Q: The graph of the derivative f' of a function f is shown

The graph of the derivative f' of a function f is shown. (a). On what intervals is f increasing? Decreasing? (b). At what values of x does f have a local maximum? Local minimum? (c). If i...

Q: Explain the difference between an absolute minimum and a local minimum.

Explain the difference between an absolute minimum and a local minimum.