By graphing the function f(x) = (tan 4x)/x and zooming in toward the point where the graph crosses the y-axis, estimate the value of lim x→0 f(x).

Use transformations of the graph of $y = \frac { 1 } { x }$ or $y = \frac { 1 } { x ^ { 2 } }$ to graph each rational function f(x). $f ( x ) = \frac { 3 x ^ { 2 } + 18 x + 28 } { x ^ { 2 } + 6 x + 9 }$

Calculate the following quantities or say why it is impossible. Let $\vec{r} = x\vec{i} + y\vec{j} + z\vec{k}$ and let $\vec{a} = a_1\vec{i} + a_2\vec{j} + a_3\vec{k}$ be a constant vector.

grad( $\vec{r} \times \vec{a}$)

Prove that each identity holds for all permissible values of x.

$$\begin{array}{l}{\text { a) } 1+\cot ^{2} x=\csc ^{2} x} \\ {\text { b) } \tan x=\csc 2 x-\cot 2 x} \\ {\text { c) } \sec x+\tan x=\frac{\cos x}{1-\sin x}} \\ {\text { d) } \frac{1}{1+\cos x}+\frac{1}{1-\cos x}=2 \csc ^{2} x}\end{array}$$

Find the derivatives of the functions in the ff exercise.

$$v=(1-t)(1+t^2)^{-1}$$

Evaluate the limit. lim x→0 tan 4x/x + sin 2x

Draw the trajectories of seven rays that leave the object heading toward the seven dots on the boundary. Assume $n_2<n_1$ and $\theta_{{c}}=45^{\circ}$.

Indicate whether the following statement is true (T) or false (F).

Semicolons and colons are always placed before closing quotation marks.

A baseball is thrown from the outfield toward the catcher. When the ball reaches its highest point, which statement is true?

Should the multiple regression equation be used for predicting the LDL cholesterol level based on weight and diastolic blood pressure? Why or why not?

Based on background knowledge you acquired in Act I and earlier in Act II, what chance do you think Elizabeth stands in defending herself against Abigail's accusations? Explain, providing supporting evidence.

The data is below:

$$\begin{array}{r|rrrrr} x_i & 2 & 6 & 9 & 13 & 20 \\ \hline y_i & 7 & 18 & 9 & 26 & 23 \end{array}$$

The estimated regression equation for these data is $\hat{y}=7.6+.9 x$. What percentage of the total sum of squares can be accounted for by the estimated regression equation? What is the value of the sample correlation coefficient?

Calculate the derivatives of the functions. $f(x)=\left[(6.4 x-1)^{2}+(5.4 x-2)^{3}\right]^{2}$

Choose the correct answer.

Management is (a) adverse, (b) averse to any decrease in employee health benefits.