For each of the following combinations of a fundamental musical tone and some of its overtones, make a computer plot of individual harmonics (all on the same axes) and then a plot of the sum. Note that the sum has the period of the fundamental $\cos 2 \pi t+\cos 4 \pi t+\frac{1}{2} \cos 6 \pi t$

f(x) is continuous on $(-\infty, \infty)$. Use the given information to sketch the graph of f.

$$\begin{aligned}&f(0)=2, f(1)=0, f(2)=-2\\&f^{\prime}(0)=0, f^{\prime}(2)=0\\&f^{\prime}(x)>0 \mathrm\ { on }\ (-\infty, 0) \mathrm\ { and }\ (2, \infty)\\&f^{\prime}(x)<0 \mathrm\ { on }\ (0,2)\\&f^{\prime \prime}(1)=0\\&f^{\prime \prime}(x)>0 \mathrm\ { on }\ (1, \infty)\\&f^{\prime \prime}(x)<0 \mathrm\ { on }\ (-\infty, 1)\end{aligned}$$

Find the Fourier sine transform of the function in the indicated problem, and write f(x) as a Fourier integral. Verify that the sine integral for f(x) is the same as the exponential integral found previously.

$$f(x)=\left\{\begin{array}{rr} -1, & -\pi<x<0 \\ 1, & 0<x<\pi \\ 0, & |x|>\pi \end{array}\right.$$

What is the process of allocating the cost of natural resources to expense as they are used?

Explain how the graph of each function can be obtained from the graph of $y=\frac{1}{x}$ or $y=\frac{1}{x^{2}}$. Then graph f and give the increasing. $f(x)=-\frac{3}{x}$

Test the following series for convergence or divergence. Decide for yourself which test is easiest to use, but don’t forget the preliminary test. Use the facts stated above when they apply. $\sum_{n=1}^{\infty} \frac{(-1)^{n}}{2^{\ln n}}$

Solve each set of equations by the method of finding the inverse of the coefficient matrix.

$$\left\{\begin{array}{rr} x-y+z= 4 \\ 2 x+y-z= -1 \\ 3 x+2 y+2 z= 5 \end{array}\right.$$

For the situation described in the previous question, which cart experiences the greater change in kinetic energy? Each cart has the same change in kinetic energy.

Solve each equation using completing the square. $x^{2}-7 x+12=0$

A harmonic oscillator is described by the function x(t) = (0.200 m) cos (0.350t). Find the oscillator's position.

A person's basal metabolic rate (BMR) is the rate at which energy is expended while resting in a neutrally temperate environment. A typical BMR is $7.00 \times 10^{6}$ J/day. Convert this BMR to units of watts. Find the rate of change of the object's height in m/s.

A cosmic ray travels 60 km through the earth’s atmosphere in $400 \mu \mathrm{s}$, as measured by experimenters on the ground. How long does the journey take according to the cosmic ray?

A person standing 1.00 m from a portable speaker hears its sound at an intensity of $7.50 \times 10^{-3} \mathrm{W} / \mathrm{m}^{2}$. Find the decibel level at a distance of 35.0 m.

The rainbow of visible colors in the electromagnetic spectrum varies continuously from the longest wavelengths (the reddest colors) to the shortest wavelengths (the deepest violet colors) our eyes can detect. Wavelengths near 655 nm are perceived as red. Those near 515 nm are green and those near 475 nm are blue. Calculate the frequency of light with a wavelength of 475 nm.