Find the Taylor series about the indicated center and determine the interval of convergence. $f(x)=\frac{1}{x}, c=1$

To increase the efficiency of a heat engine, would it be better to increase the temperature of the reservoir while holding the temperature of the sink constant, or to decrease the temperature of the sink while holding the temperature of the reservoir constant? Show your work.

Determine whether y is a function of x

$$x=9-y^{2}$$

Atomic size seems to play an important role in explaining some of the differences between the first element in a group and the subsequent group elenents. Explain.

Find the x-intercept and the y-intercept of the graph of each equation. Then graph the equation using the intercepts.

$$4x-3y+12=0$$

The Apex Plastics Corp. finds a new way to produce plastic outdoor furniture from recycled milk bottles at very low cost. What will happen to the supply curve for plastic furniture? Explain your answer.

What opportunities are offered to Elise and her mother? What do they do with these opportunities?

A sandbox has an area of 26 square feet, and the length is 5$\frac{1}{2}$ feet What is the width of the sandbox?

Name each property shown. (3+2)(4)=(4)(3+2)

What does the first law of thermodynamics tell us about the energy of the universe?

Use a known Taylor polynomial with n nonzero terms to estimate the value of the integral. $\int_{-1}^{1} \frac{\sin x}{x} d x, n=3$

Determine the radius and interval of convergence. $\sum_{k=1}^{\infty} \frac{k^{2}}{2^{k}}(x+2)^{k}$

Determine convergence or divergence of the series. $\sum_{k=1}^{\infty} \frac{e^{1 / k}+1}{k^{3}}$

Determine convergence or divergence of the series. $\sum_{k=1}^{\infty} \frac{1}{\cos ^{2} k}$