Evaluate the integrals. Check your results by differentiation.

$$\int \frac{3 x^4 d x}{\left(2 x^5\ -\ 5\right)^4}$$

For each of the following, make the indicated conversion, showing explicitly the conversion factor(s) you used.

b. $9.216 \mathrm{~cm}$ to millimeters

Why does Odysseus go to the Land of the Dead?

Find limit $\lim _{x \rightarrow 0} \frac{\cot 2 x}{\csc x}$.

Determine whether it's true or false.

To determine if 907 is prime, you only need to check if 907 is divisible by the prime numbers between 1 and 31.

Even though the limit can be found using algebraic simplification as in Section $10.1$, use $L’H\^{o}pital’s$ rule to find the limit.

$$\lim\limits_{x\to{-1}} \dfrac{x+1}{x^{2}-7x-8}$$

Monochromatic light of wavelength l is incident on a pair of slits separated by $2.40 \times 10 ^ { - 4 }$ m, and forms an interference pattern on a screen placed 1.80 m away from the slits. The first-order bright fringe is 4.52 mm from the center of the central maximum. Find the angle corresponding to the first-order bright fringe and compute the sine of that angle. Are the sine and tangent of the angle comparable in value? Does your answer always hold true?

Describe the energy conversions that happen in a swinging pendulum

Express the limit as an equivalent limit in which $x \rightarrow 0 ^ { + }$ or $x \rightarrow 0 ^ { - } ,$ as appropriate. [You need not evaluate the limit].
(a)$\lim _ { x \rightarrow + \infty } \frac { \cos ( \pi / x ) } { \pi / x }$
(b)$\lim _ { x \rightarrow + \infty } \frac { x } { 1 + x }$
(c) $\lim _ { x \rightarrow - \infty } ( 1 + 2 x ) ^ { 1 / x }$

In this exercise, you will need to use the information given below to evaluate the limits.

$$\lim _{x \rightarrow c} f(x)=16$$

$$\lim _{x \rightarrow c} \sqrt{f(x)}$$

In the presence of a tungsten catalyst at high temperatures, the decomposition of ammonia to nitrogen and hydrogen is a zero-order process. If the rate constant at a particular temperature is $3.7 \times 10^{-6} \mathrm{~mol}(\mathrm{~L} \cdot \mathrm{s})$, how long will it take for the ammonia concentration to drop from an initial concentration of $5.0 \times 10^{-4} \mathrm{M}$ to $5.0 \times 10^{-5} \mathrm{M}$ ? What is the half-life of the reaction under these conditions?

Find the limit (if it exists). If the limit does not exist, explain why. Use a graphing utility to verify your result graphically. $\lim _{x \rightarrow-\infty} \frac{4 x^{2}-3}{2-x^{2}}$

How does a nuclear reactor produce electricity?

convert each angle measure to decimal degree form without using a calculator. Then check your answers using a calculator. 54° 45’