Write each complex number in polar form. Then use either (4) or (5) to obtain a polar form of the given number. Write the polar form in the form $a+i b$. $\frac{-i}{2-2 i}$

Decide whether the function is one-to-one.

$$y=-2 x^5-4$$

Suppose that $f(t)$ and $f(t)$ are defined for all $t$ and that $\lim _{t \rightarrow t_0} f(t)=-7$ and $\lim _{t \rightarrow t_0} g(t)=0$. Find the limit as $t \rightarrow t_0$ of the following function:

$$f(t)+g(t)$$

Underline the form of rise or raise in each of the following sentences. If the form is already correct, write C above it. If the form is not correct, write the correct form above it.

In the barn, stacks of hay bales raise to the rafters.

If $u(t)=i-2 t^2 j+3 t^3 k$ and $v(t)=t i+\cos t j+\sin t k$, find $D_t[u(t) \cdot \mathbf{v}(t)]$.

Write an equation in point-slope form, slope-intercept form, and standard form for the given line.

$$(-5,7),(3,1)$$

Underline the form of sit or set in each of the following sentences. If the form is already correct, write C above it. If the form is not correct, write the correct form above it

From his highchair he could reach the food that was sitting nearby.

Find T(t), N(t),

$$a_T$$

, and

$$a_N$$

at the given time t for the space curve r(t). [Find a(t), T(t),

$$a_T$$

, and

$$a_N$$

. Solve for N in the equation

$$a(t) = a_T T + a_N N$$

.] Vector-Valued Function: r(t) = ti + 2tj - 3tk Time: t = 1

Describe one similarity and one difference between photosynthesis and chemosynthesis.

Find a basis for each of the following subspaces of $\mathbf{R}^3$. Give the dimension of each subspace.

(a) the set of vectors of the form $(a, a, b)$ (b) the set of vectors of the form $(a, a, 2 a)$ (c) the set of vectors of the form $(a, b, a+b)$ (d) the set of vectors of the form $(a, 2 b, a+3 b)$ (e) the set of vectors of the form $(a, b, c)$ where $a+b+c=0$

Show that the function $f(x)=3(x-5)^2+7$ is not one-to-one.

Which of the following is an example of a marketing intermediary?

A. An agency that operates at a federal level and has a centralized distribution system

B. A not-for-profit body that aims at product distribution through charitable channels

C. A retailing agency that purchases products from manufacturers to resell at a profit

D. An independent business unit that manufactures its products by purchasing raw materials from other agencies

Locate and classify all the critical points of the functions. $h(x, y)=x^{2}+y^{2}-y^{2} x-4$

Classify the critical points of the functions using the Second Derivative Test whenever possible. $f(x)=x e^{x}$