Find all vertical asymptotes. $f(x)=\frac{x^{2}+1}{x^{3}+3 x^{2}+2 x}$

Set up an integral for the area of the surface generated by revolving the given curve about the indicated axis. $x y=1, \quad 1 \leq y \leq 2 ; \quad y \text {-axis }$

Use the result of the previous part to find the volume of the solid generated by revolving each plane region about the y-axis. (Hint: Begin by approximating the points of intersection.)

Find a point-slope form of the line satisfying the conditions. Use the first point given for $\left(x_1, y_1\right)$. Then convert the equation to slope-intercept form, and write the formula for a function $f$ whose graph is the line.

$x$-intercept $(-2,0), y$-intercept $(0,5)$

Sketch $(1, −2, 3)$ and $\left(-\frac{1}{3},\frac{2}{3},-1\right)$. Why do these vectors point in opposite directions?

A solid S is generated by revolving the region between the x-axis and the curve y=

$$\sqrt { \sin x } ( 0 \leq x \leq \pi )$$

about the x-axis. An integral expression for the volume of S is ___.

Find the volume generated by revolving the regions bounded by the given curves about the $x$-axis. Use the indicated method in each case.

$y=x^2+1, y = x + 1$ (shells)

Write in the blank whether the sentence is simple or compound.

Lauren is sweeping the dugout, and Kat is cleaning the bases.

Graph the parabola by hand, and check using a graphing calculator: Give the vertex, axis, domain, and range.

$$y=(x+3)^2-4$$

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line $y=4$.

$$y=\sqrt{3 x}+4, \quad y=4, \quad x=3$$

Write and evaluate the definite integral that represents the area of the surface generated by revolving the curve on the indicated interval about the y-axis. $y=\frac{x^{2}}{2}+4$, $0 \leq x \leq 2$

Find the volume of the solid generated by revolving the region in the irst quadrant bounded by the coordinate axes and the curve

$$y = \cos x , 0 \leq x \leq \pi / 2$$

about

the line

$$x = \pi / 2.$$

In this exercise, find the volume of the solid generated by revolving the plane region bounded by the equations about the indicated line(s).

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

the $x$-axis

For 20a-20b, choose Yes or No to indicate whether the first digit of the quotient is in the hundreds place. 20a.

$$1,523 \div 23$$

20b.

$$2,315 \div 9$$