Differentiate the series

$$E(x)=\sum_{n=0}^{\infty} \frac{x^{n}}{n !}$$

term-by-term to show that E(x) is equal to its derivative.

Evaluate the quotient in the following problem.

-144 $\div$ (- 24)

Make a conjecture about the pattern. Write the next two items.

$\dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{8},$-3,6,-9,12, \ldots$

Find $\int_{0}^{x} f(u) d u$ by integrating term by term.

$$f(x)=\sum_{k=1}^{\infty} \frac{x^{k}}{k}$$

Why does the narrator cry when everyone congratulates him for teaching Doodle to walk?

Consider the following pattern: $\frac{1}{2^{3}}=\frac{1}{8}, \frac{1}{2^{2}}=\frac{1}{4}, \frac{1}{2^{1}}=\frac{1}{2}, \frac{1}{2^{0}}=1$. Continue the pattern to find $\frac{1}{2^{-1}}, \frac{1}{2^{-2}}, \frac{1}{2^{-3}},$ and $\frac{1}{2^{-4}}$.

Which archipelago did the Ortoiroid people settle around 2 000 BCE?

The man credited with teaching the Patriots how to fight professionally is?

The nth term of a sequence is given. Find the indicated term. $c_{n}=5 n-4 ; \text { find } c_{157}$

Describe the difference between finding work done by a constant force and finding the work done by a variable force.

Identify the equation given as separable, homogeneous, first-order linear, or exact, and then solve. A change of variable may be needed to put the given equation into one of these forms.

$$\left(3 x^{2}-y \sin x y\right) d x-(x \sin x y) d y=0$$

Match the correct answer.

Assess blood flow to the kidneys $\rule{4cm}{0.15mm}$

Tests and Procedures:

a. dialysis

b. transplant

c. KUB

d. retrograde pyelogram

e. cystoscopy

f. nephrolithotomy

g. nephrectomy

h. needle aspiration

i. renal angiogram

j. lithotripsy

Use Cramer's rule to solve

$$\left\{\begin{array}{l} x=x^{\prime} \cos \theta-y^{\prime} \sin \theta \\ y=x^{\prime} \sin \theta+y^{\prime} \cos \theta \end{array}\right.$$

for $x^{\prime}, y^{\prime}$ in terms of x and y.

$Professor$ is to $teaching$ $assistant$ as $lawyer$ is to_____.