The parametric curve x = 2 cos (-t), y = 2 sin (-t),0 ≤ t ≤ 2π is traced clockwise. Justify your answer.

Use the Divergence Theorem to calculate the surface integral ∫∫S F · dS; that is, calculate the flux of F across S.

$$F(x, y, z) = x^2yz i + xy^2z j + xyz^2 k$$

S is the surface of the box enclosed by the planes x = 0, x=a, y=0, y=b, z=0 and z=c, where a, b, and c are positive numbers

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y sin 2x = x cos 2y, (π/2, π/4)

Select the representations that do not change the location of the given point.

$$\left( 2 , - \frac { 3 \pi } { 4 } \right)$$

$$a. \ \left( 2 , - \frac { 7 \pi } { 4 } \right) \\ b. \ \left( 2 , \frac { 5 \pi } { 4 } \right) \\ c. \ \left( - 2 , - \frac { \pi } { 4 } \right) \\ d. \ \left( - 2 , - \frac { 7 \pi } { 4 } \right)$$

Sketch a graph of the polar equation.

$$r = 2 \sin 5 \theta$$

The graph of the parametric curve x = 3 cos t, y = 4 sin t is a circle. Justify your answer.

Rewrite the exponential expression to have the indicated base. 16³ˣ, base 2

If John invests $2300 in a savings account with a 6% interest rate compounded annually, how long will it take until John’s account has a balance of$4150?

Two identical asteroids travel side by side while touching one another. If the asteroids are composed of homogeneous pure iron and afe spherical, what diameter in feet must they have for their mutual gravitational attraction to be 1 lb?

Find the graph the function.

$$y=\left\{\begin{array}{lr}\sqrt{-x}, & -4 \leq x \leq 0 \\ \sqrt{x}, & 0<x \leq 4\end{array}\right.$$

Use appropriate substitutions to write down the Maclaurin series for the given binomial. $(1-x)^{1 / 3}$

Find the range

$$y=\left\{\begin{array}{lr}\sqrt{-x}, & -4 \leq x \leq 0 \\ \sqrt{x}, & 0<x \leq 4\end{array}\right.$$

How many terms of the Maclaurin series for ln(1 + x) do you need to use to estimate ln 1.4 to within 0.001?

Compute the first four partial sums $S _ { 1 } , \ldots , S _ { 4 }$ for the series having nth term $a_n$ starting with n = 1 as follows. $a _ { n } = 1 / n$