Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved about the given axis. If possible, find the volume of S by both the disk/washer and shell methods. Check that your results agree and state which method is easier to apply. y=x-

$$x^4$$

, y=0; revolved about the y-axis

Compute the first-order partial derivatives.

$$W = e ^ { r + s }$$

Consider the molecule $BF_3.$ What is the electron configuration of an isolated B atom?

Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved about the given axis. If possible, find the volume of S by both the disk/washer and shell methods. Check that your results agree and state which method is easier to apply. y=6/(x+3), y=2-xl revolved about the x-axis

Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved about the given axis. If possible, find the volume of S by both the disk/washer and shell methods. Check that your results agree and state which method is easier to apply. y=1/(x+1), y=1-x/3; revolved about the x-axis

Find the antiderivative. $\int x \ln \left(x^{2}\right) d x$

Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved about the given axis. If possible, find the volume of S by both the disk/washer and shell methods. Check that your results agree and state which method is easier to apply. y=x-

$$x^4$$

, y=0; revolved about the x-axis

Disks/washers about the $\boldsymbol{y}$-axis Let $R$ be the region bounded by the following lines and curves. Use the disk or washer method to find the volume of the solid generated when $R$ is revolved about the y-axis. \

$$y=0, y=\sqrt{x-1}, y=2, x=0$$

Disk method Let R be the region bounded by the following curves. Use the disk method to find the volume of the solid generated when R is revolved about the $x$-axis.
$y=4-x^2, y=0, x=0$

A substance produced in one part of a plant that affects another part is a(an) a. hormone. b. enzyme. c. auxin. d. phytochrome.

Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved about the given axis. If possible, find the volume of S by both the disk/washer and shell methods. Check that your results agree and state which method is easier to apply. y=

$$( x - 2 ) ^ { 3 }$$

-2, x=0, and y=25; revolved about the y-axis

Evaluate using the identity

$$a ^ { 3 } - b ^ { 3 } = ( a - b ) \left( a ^ { 2 } + a b + b ^ { 2 } \right)$$

$$\lim _ { x \rightarrow 2 } \frac { x ^ { 3 } - 8 } { x - 2 }$$

Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved about the given axis. If possible, find the volume of S by both the disk/washer and shell methods. Check that your results agree and state which method is easier to apply. y=

$$x^2$$

, y=2-x, and x=0 in the first quadrant; revolved about the y-axis.

In "The House on Mango Street," what does Esperanza mean when she refers to her home as "the house I belong but do not belong to"?