Find

$$\sin \frac { \theta } { 2 } , \cos \frac { \theta } { 2 } , \text { and } \tan \frac { \theta } { 2 }$$

for the set of conditions.

$$\sin \theta = - \frac { 24 } { 25 } \text { and } 180 ^ { \circ } < \theta < 270 ^ { \circ }$$

Find the oblique asymptote, and sketch the graph of $\boldsymbol{f}$.

$$f(x)=\frac{2 x^2-x-3}{x-2}$$

Find the exact value.

Find $\sin (2 \theta), \cos (2 \theta)$, and $\tan (2 \theta)$ given $\cos \theta=-\frac{1}{3}$ and $\theta$ is in the interval $\left[\frac{\pi}{2}, \pi\right]$

(a) Use a graph of

$$f(x)=\left(1-\frac{2}{x}\right)^x$$

to estimate the value of $\lim _{x \rightarrow \infty} f(x)$ correct to two decimal places. (b) Use a table of values of $f(x)$ to estimate the limit to four decimal places.

Find the oblique asymptote and sketch the graph of each rational function.

$$f(x)=\frac{2 x^2-x}{x-1}$$

A particle moves according to a law of motion s=f(t) where $s=\sqrt{t}\left(3 t^2-35 t+90\right)$, $t \geqslant 0$, where t is measured in seconds and s in feet. Find the velocity at time t.

(a) Why do you think it is important to store standard solutions in sealed containers?

(b) Predict the effect on the concentration of a sodium chloride solution if it is stored in an open container. Use the equation $c=\frac{n}{V}$ in your answer.

Find coordinates of points that tell the location of the Ferris wheel seat that begins at point A(1,0) when the wheel undergoes the following rotations. Record the results on a sketch that shows a circle and the points with their coordinate labels. a. $\theta=30^{\circ}$ b. $\theta=70^{\circ}$ c. $\theta=90^{\circ}$ d. $\theta=120^{\circ}$ e. $\theta=140^{\circ}$ f. $\theta=180^{\circ}$ g. $\theta=220^{\circ}$ h. $\theta=270^{\circ}$ i. $\theta=310^{\circ}$

Cindy bought pencils and erasers in a store. The number of pencils was $6$ less than $4$ times the number of erasers. Cindy bought $3$ erasers. Write an equation for how many pencils Cindy bought and solve.

Find

$$\sin \frac { \theta } { 2 } , \cos \frac { \theta } { 2 } , \text { and } \tan \frac { \theta } { 2 }$$

for the set of conditions.

$$\sin \theta = - \frac { 3 } { 5 } \text { and } 180 ^ { \circ } < \theta < 270 ^ { \circ }$$

Determine whether the statement is true or false. Explain your answer. The function

$$f ( x ) = e ^ { - x } + 1$$

is a solution to the initialvalue problem

$$\frac { d y } { d x } = - \frac { 1 } { e ^ { x } } , \quad y ( 0 ) = 1$$

A store sells roasted peanuts in 1, 2, 2.5, and 4 pound bags. The peanuts cost $4 per pound. Write an equation in function notation that represents the cost of the peanuts in terms of the number of pounds, and graph the function.

Write a dialogue between two people in Nebraska who are expressing their views on the issue of popular sovereignty. Have one person defend the policy and the other oppose it.

In an experiment, caterpillars consumed 8 grams of lettuce leaves and 0.4 grams of tomato leaves.