Questions from General Calculus

Q: Find the 50th derivative of y = cos 2x.

Find the 50th derivative of y = cos 2x.

Q: Find the 1000th derivative of f (x) = xe-

Find the 1000th derivative of f (x) = xe-x.

Q: The displacement of a particle on a vibrating string is given by

The displacement of a particle on a vibrating string is given by the equation s (t) = 10 + 1/4 sin (10πt) where is measured in centimeters and in seconds. Find the velocity of the particle after secon...

Q: The table gives the US population from 1790 to 1860.

The table gives the US population from 1790 to 1860. (a). Use a graphing calculator or computer to fit an exponential function to the data. Graph the data points and the exponential model. How good...

Q: If the equation of motion of a particle is given by s

If the equation of motion of a particle is given by s = A cos (wt + δ), the particle is said to undergo simple harmonic motion. (a). Find the velocity of the particle at time t. (b). When is the veloc...

Q: A Cepheid variable star is a star whose brightness alternately increases and

A Cepheid variable star is a star whose brightness alternately increases and decreases. The most easily visible such star is Delta Cephei, for which the interval between times of maximum brightness is...

Q: (a). The graph of a position function of a car

(a). The graph of a position function of a car is shown, where s is measured in feet and t in seconds. Use it to graph the velocity and acceleration of the car. What is the acceleration at t = 10 seco...

Q: Trace or copy the graph of the given function f. (

Trace or copy the graph of the given function f. (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of f' below it.

Q: Let be the tangent line to the parabola y = x2 at

Let be the tangent line to the parabola y = x2 at the point (1, 1). The angle of inclination of l is the angle ø that l makes with the positive direction of the x-axis. Calculate ø correct to the near...

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 it is known...