1) Sketch the graph of the function ℎ(?) = ?^5⁄3 − 5?^2⁄3 , showing all work for domain, intercepts, asymptotes, increase/decrease, relative extrema, and concavity.

2) For the function ?(?) = 2?^2−6/(?−1)^2 , find a) all intercepts, and b) all asymptotes.

3) Determine the concavity of the function ?(?) = ?^2?^−? .

4) Use properties of logarithms to rewrite the expression below as a sum, difference, or multiple of logarithms. ln ?(rad 3)√?^2 + 1 3

5) Use properties of logarithms to rewrite the expression below as the logarithm of a single quantity. 5 ln(? − 6) + 1/2 ln(4? + 1)

For #6-8, find ?? ?? .

6) ? = (?^2 + 1)?^4?

7) ? = ln √(?+1/?−1)

8) 30 = ln(??) + 5?

9) Find an equation of the tangent line to the graph of the function ?(?) = ln 5(?+2)/? at the point (− 5/2 , 0). Write your answer in slope-intercept form.

1) Draw the curve and indicate with an arrow the direction in which it goes when t increases. Delete the parameter to find the Cartesian equation. x = 3t-1, y = 2t +1

2)Draw the curve and indicate with an arrow the direction in which it goes when t increases. Delete the parameter to find the Cartesian equation. x= e^t , y = e^(3t)+1

Given two lines, state and prove the precise conditions under which reflecting a point about the two lines is commutative.

I have seen this proved on here more than once, but I do not understand the answers that have been provided. I have seen that the two lines must be perpendicular- Why isn't it all sets of two lines? Is there a counterexample that I can visualize? Is that answer even correct? Thank you!

1. Use the function to find the following values (or state that they do not exist): f(x) = 2 (x + 1)2 (x + 1)(x − 1)(x + 2)

(a) State the domain of f(x).

(b) Find any removable discontinuities (holes in the graph).

(c) Find any Vertical Asymptotes.

(d) Find any x-intercepts.

(e) Find any y-intercepts.

(f) Find the Horizontal Asymptote. Explain how you determined that this was an asymptote.

(g) Graph f(x). Hint: It may help to find f(−3) and f(2).

1.  Suppose c = 15 and A = 35 degrees.

Find:

a=

b=

B=

2. Suppose a = 12 and b = 11.

Find an exact value or give at least two decimal places:

sin(A)=

cos(A) =

tan(A) =

sec(A)=

csc(A)=

cot(A)=

Consider F and C below.

F(x, y, z) = yz i + xz j + (xy + 14z) k

C is the line segment from (3, 0, −3) to (5, 5, 1)

(a) Find a function f such that F = ∇f.

f(x, y, z) =

(b) Use part (a) to evaluate

∇f · dr along the given curve C.

Given the two lines

(x, y, z) = (4, -3, 5) + t(2, 0, -3)

(x, y, z) = (4, -3, 5) + s(5, 1, -1)

a) determine a vector equation for the plane that combines the two lines

b) parametric equations of the plane that contains the two lines

c) Cartesian equation of the plane that contains the two lines

1. Given the series:

∞∑k=1 2/k(k+2)
does this series converge or diverge?

• converges
• diverges

If the series converges, find the sum of the series:

∞∑k=1 2/k(k+2)=

2. Given the series:

1+1/4+1/16+1/64+⋯
does this series converge or diverge?

• diverges
• converges

If the series converges, find the sum of the series:

1+1/4+1/16+1/64+⋯=

Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare your answer with the value of the integral produced by your calculator. (Round your answer to six decimal places.)

y = e^−x^2, 0 ≤ x ≤ 5

Use spherical coordinates to find the volume of the solid E that lies below the cone z = sqrt x^2 + y^2, and within the sphere x^2 + y^2 + z^2 = 2, in the first octant.

don't do incomplete or wrong I am already stressed, explain the shifting of all types for fx graph I will not tolerate wrong

f(x) = x⁴ − 128x² + 7

(a) Find the intervals on which f is increasing or decreasing. (Enter your answers using interval notation.)

(b) Find the local maximum and minimum values of f. (If an answer does not exist, enter DNE.)

(c) Find the intervals of concavity and the inflection points. (Enter your answers using interval notation.)

In the 3-month period November 1, 2014, through January 31, 2015, Hess Corp. (HES) stock decreased from $80 to $64 per share, and Exxon Mobil (XOM) stock decreased from $96 to $80 per share. If you invested a total of $26,880 in these stocks at the beginning of November and sold them for $22,080 3 months later, how many shares of each stock did you buy?

Hess Corp. (HES) stock  shares

Exxon Mobil (XOM) stock

QUESTION 1

A. Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 11 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is given by V= 1/3 pi r^2h. When the pile is 11 feet high, its height is increasing at _______ feet per minute.

B.A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5ft/sec along a straight path. How fast is the tip of her shadow moving along the ground when she is 50 ft from the base of the pole? ______ft/sec How fast is the length of her shadow increasing? ______ft/sec

C. Water is leaking out of an inverted conical tank at a rate of 0.0087 m^3/min. At the same time water is being pumped into the tank at a constant rate. The tank has height 12 meters and the diameter at the top is 6 meters. If the water level is rising at a rate 0.19 m/min when the height of the water is 4.5 meters, find the rate at which water is being pumped into the tank. Water is being pumped in at _____m^3/min.

D. The tip of a 27 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 2 feet per second. How fast is the bottom of the ladder sliding along the ground when the bottom of the ladder is 10 feet away from the base of the ball?

E. A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2cm/min. At what rate is the volume of the snowball decreasing when the diameter is 17cm? (Answer is positive number)