Let D be the region bounded below by the plane z = 0, above by the sphere

$$x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4,$$

and on the sides by the cylinder

$$x ^ { 2 } + y ^ { 2 } = 1.$$

Set up the triple integrals in cylindrical coordinates that give the volume of D using the following orders of integration.

$$d z\ d r\ d \theta$$

Use a double integral in polar coordinates to find the volume of the solid bounded by the graphs of the equations. -Inside the hemisphere z = √16 - x² - y² and outside the cylinder x² + y² = 1

Find the volume of the region bounded below by the plane z = 0, laterally by the cylinder

$$x ^ { 2 } + y ^ { 2 } = 1$$

and above by the paraboloid

$$z = x ^ { 2 } + y ^ { 2 }.$$

Determine whether the series is convergent or divergent. $\sum_{n=1}^{\infty} \frac{n^{2 n}}{\left(1+2 n^{2}\right)^{n}}$

Leila drops a ball from a height of 1 meter. The height of each bounce is 75% of the previous height. a. What is the ball's height after the first bounce? b. What rule can be used to find the ball's height after n bounces? c. What is the height of the sixth bounce? Round your answer to the nearest hundredth.

Solve the following exercise. Evaluate the integral or show that it is divergent.

$$\int_0^{\pi / 2} \cos ^3 x \sin 2 x d x$$

How could you sketch the inverse of an exponential function?

List the body's nonspecific defenses against pathogens.

You are given the dollar value of a product in 2012 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 0 represent 2010.) 2012 Value: $1850 Rate:$250 increase per year

In the following exercise, show that the given series below is divergent.

$$\sum_{n=1}^{\infty} \frac{n}{\sqrt{2 n^2+1}}$$

Let D be the solid region bounded below by the plane z=0, above by the sphere $x^2+y^2+z^2=4$, and on the sides by the cylinder $x^2+y^2=1$. Set up the triple integrals in cylindrical coordinates that give the volume of D using the following orders of integration.

$$d \theta d z d r$$

Complete the sentence by writing the correct form of the word shown in parentheses. You may not need to change the form that is given.

The argument lacked........... and fell apart like a house of cards in an earthquake. (cohere)

In the said chapter we used a geometrical argument to prove that

$$\lim _{\theta \rightarrow 0} \frac{\sin \theta}{\theta}=1 .$$

Express the ratio R of the area of $\triangle A B D$ to that of the shaded region.

For the following exercises, find the inverse of the function.
$f(x)=3 x-5$