Calculate $\frac{d y}{d x}$. You need not expand your answers. $y=\frac{3 x-1}{(x-5)(x-4)(x-1)}$

Let $G$ be an Abelian group and $H = \{ x \in G | | x |$ is 1 or even $\} .$ Give an example to show that $H$ need not be a subgroup of $G .$

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

a) Determine the load impedance for the circuit shown in Fig. that will result in maximum average power being transferred to the load if $\omega=5 \mathrm{krad} / \mathrm{s}$. b) Determine the maximum average power delivered to the load from part (a) if $v_g=$ $80 \cos 5000 t \mathrm{~V}$. c) Repeat part (a) when $Z_{\mathrm{L}}$. consists of two components from Appendix $\mathrm{H}$ whose values yield a maximum average power closest to the value calculated in part (b).

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

Use the geometric series

$$f ( x ) = \frac { 1 } { 1 - x } = \sum _ { k = 0 } ^ { \infty } x ^ { k }$$

, for |x|<1, to find the power series representation for the following functions (centered at 0). Give the interval of convergence of the new series.

If you want to tile the kitchen with $12" \times 12"$ tiles, how many tiles will you need to buy?

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

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

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 $\delta_{\max }=0.125\ \mathrm{in}$.

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 $50 \mathrm{~mm}$.

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

Use a graphing utility to graph the power series. The series represents a well-known function. Identify the function from the graph of its power series.

$$f(x)=\sum_{n=0}^{\infty}(-1)^n x^n, \quad-1<x<1$$

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