Graph each function on the interval $[-2 \pi, 2 \pi]$. For the trigonometric functions, explain how the graphs are transformations of $y=\sin x$ or $y=\cos x$.

$$H(x)=-\frac{1}{3} \sin x$$

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

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).

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

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

An element has two naturally occurring isotopes. The isotope has a mass of 62.9396 amu and a relative abundance of 69.17 %, and isotope 2 has a mass of 64.9278 amu.

Find the atomic mass of this element.

How are computers used in pavement management?

The vertices of a triangle are A(2, 5), B(1, 2), and C(3, 1). Find the coordinates of the image after the transformations given. Reflect in the x-axis, and then rotate $90^{\circ}$ counterclockwise about the origin.

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

Evaluate the expression. -6 + 3 - (-1) + 11

Find the derivatives of the functions in the ff exercise

$$k(x)=x^2 \sec (\frac{1}{x})$$

Find the indicated derivatives.

$$\frac{dy}{dx}\quad\text{if}\quad y=\frac{3x-4}{12x^2}$$

Choose the correct answer.

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

Express each quadratic function in the form $f(x)=a(x-h)^2+k$. Then use transformations of the graph of $f(x)=x^2$ to graph each function.

$$f(x)=-\frac{1}{2} x^2+4 x-2$$

Find the sum. -41 + 26