Find the Taylor series for the functions defined as follows. Give the interval of convergence for each series. $f(x)=\frac{7 x}{1+2 x}$

Find the payments necessary to amortize each loan. $2500, 16% compounded quarterly, 6 quarterly payments

This problem concerns the surface described by the equation $(r − 2)^2 + z^2 = 1$ in cylindrical coordinates. (Assume $r \geq 0$.) (a) Sketch the intersection of this surface with the halfplane $\theta=\pi / 2$. (b) Sketch the entire surface.

Find the Taylor series for the functions defined as follows. Give the interval of convergence for each series. $f(x)=\frac{e^{x}-e^{-x}}{2}$

Evaluating the integral

$$\int_{-\infty}^{\infty} \frac{10 \delta(\omega)}{4+\omega^{2}} d \omega$$

results in: (a) 0 (b) 2 (c) 2.5 (d) $\infty$

Find Taylor polynomials of degree 4 at 0 for the functions defined as follows. $f(x)=5 e^{2 x}$

The following definitions and program segments has errors. Locate as many as you can. char greeting[] = {'H', 'e', 'l', 'l', 'o'}; cout << greeting;

A jogger’s arm swings according to the equation $y=\frac{1}{5} \sin [\pi(t-1)]$. Proceed as directed in parts a–d of the preceding exercise, with the following exceptions: in part c, replace the differential equation with $\frac{d^{2} y}{d t^{2}}+\pi^{2} y=0$, and in part d, consider the times t=1.5 seconds, t=2.5 seconds, and t=3.5 seconds.

Use Newton’s method to approximate each radical to the nearest thousandth. $\sqrt{51.7}$

Assuming that numbers is an array of doubles, will the following statement display the contents of the array? cout << numbers << endl;

The differential equation that describes the current in an RLC network is

$$3 \frac{d^{2} i}{d t^{2}}+15 \frac{d i}{d t}+12 i=0$$

Given that i(0) = 0, di(0)/dt = 6 mA/s, obtain i(t).

The height h of the aerobic stepper is 25 cm. A 65 kg person goes up and down the step once every 2 s. Accounting only for the work done in lifting her body and assuming a muscle efficiency of 25%, determine the calories (1C = 4.184 kJ) burned by the person in 1 h.

A rumor spreads through a community of 500 people at the rate $\frac{d N}{d t}=0.02(500-N) N^{1 / 2}$, where N is the number of people who have heard the rumor at time t (in hours). Use Euler’s method with h=0.5 to find the number who have heard the rumor after 3 hours, if only 2 people heard it initially.

A 5.0-m-long rod is stretched 0.10 m by a force. What is the strain in the rod?