Find the horizontal and vertical asymptotes of the graph of the function. (You need not sketch the graph.) $g(x)=2 x^{3}+x^{2}+1$

Suppose that you want to find the Fourier series of $f(x)=x+x^{2}$. Explain why to find $b_k$ you would need only to integrate $x \sin \left(\frac{k \pi x}{l}\right)$ and to find $a_k$ you would need only to integrate $x^{2} \cos \left(\frac{k \pi x}{l}\right)$.

The tee shape shown in Figure P8.64b/65b is used as a short post to support a load of $P=4,600 \mathrm{lb}$. The load $P$ is applied at a distance of 5 in. from the surface of the flange, as shown in Figure P8.64a/65a. Determine the normal stresses at points $H$ and $K$, which are located on section $a-a$.

What factor would you need to multiply by $(3d + 1)$ to get $9 d^{2}+6 d+1 ?$

Each series satisfies the hypotheses of the alternating series test. Approximate the sum of the series to two decimal-place accuracy.

$$1 - \frac { 1 } { 2 ! } + \frac { 1 } { 4 ! } - \frac { 1 } { 6 ! } + \cdots$$

Find the horizontal and vertical asymptotes of the graph of the function. (You need not sketch the graph.) $f(x)=\frac{x^{2}-2}{x^{2}-4}$

You need to find the LCM of 13 and 14. Would you rather list their multiples or use their prime factorizations? Explain.

How many packages of each does Loren need to buy to have 24 fish fillets and 24 buns?

To win a case where the discrimination is admitted, the employee need only prove that she or he was denied employment because of membership in a(n) ?.

A cast-iron tube is used to support a compressive load. Knowing that $E=69 \mathrm{GPa}$ and that the maximum allowable change in length is $0.025 \%$. Actermine $(a)$ the maximum normal stress in the tube, $(b)$ the minimum wall thickness for a load of $7.2 \mathrm{kN}$ if the outside diameter of the tube is $50 \mathrm{~mm}$.

What is the sequence of buttons you need to press to enter the number $5.8 \times 10^{-8}$ into a scientific calculator?

A propped cantilever beam is subjected to uniform load $q$. The beam has flexural rigidity $E I=2000\ \mathrm{kip}-\mathrm{ft}^2$ and the length of the beam is $10 \mathrm{ft}$. Find the intensity $q$ of the distributed load if the maximum displacement of the beam is $\delta_{\max }=0.125\ \mathrm{in}$.

Explain why you may need less than one liter of water to prepare a molar solution of one liter.

A uniform rope of cross-sectional area 0.50 cm² breaks when the tensile stress in it reaches

$$6.00 × 10^6 N/m^2.$$

(a) What is the maximum load that can be lifted slowly at a constant speed by the rope? (b) What is the maximum load that can be lifted by the rope with an acceleration of 4.00 m/s²?