Calculus
The marketing department for a cell phone telephone company has determined that the demand for their phone obeys the following relationship: p= -0.02+200 , (0 ≤ p ≤10,000) , where p denotes the phone’s unit price (in dollars) and x the quantity demanded. This type of question is much easier when you use your calculator, I just need to know what you did when you give me an answer using it,
(a) Express the revenue as a function of x: Round all of the following answers to the nearest penny when necessary.
(b) Find the rate of change in the revenue between the 2,000th and 4,000th phone.
(c) Find the rate in change of revenue from the sale of the 5,118th phone.
(d) Find the exact revenue from the sale of the 815th telephone.
(e) Use the marginal revenue function to estimate the revenue from the sale of the 815th phone. (f) Find the average revenue from the sale of 3000 phones.

Compute the hydrostatic force on a circular plate of radius 5 meters suspended vertically in water so that the top of the plate is at the surface of the water. (The density of water is 1000 kilograms per cubic meter, and acceleration due to gravity is 9.8 meters per second squared.)

Suppose that f is a differentiable function with derivative f" (x) = (x − 3)(x + 1)(x + 5). Determine the intervals of x for which the function of f is increasing and decreasing

Explain why a positive value for f" (x) means the graph f(x) is increasing

For f(x) = 2x²- − 3x² − 12x + 21, find where f'(x) = 0, and the intervals on which the function increases and decreases

Determine the values of a, b, and c such that the graph of y = ax_². + bx + c has a relative maximum at (3, 12) and has a y-intercept at 1.

Questionnnnnnn

a. Let V and W be vector spaces and T : V → W a linear transformation. If {T(v1), . . . T(vn)} is linearly independent in W, show that {v1, . . . vn} is linearly independent in V .

b. Define similar matrices

c Let A1, A2 and A3 be n × n matrices. Show that if A1 is similar to A2 and A2 is similar to A3, then A1 is similar to A3.

d. Show that similar matrices have the same characteristic polynomial and eigenvalues.

e. Determine whether the following mappings are linear transformations.

T : V → R defined by T(x) = hx, vi, where v is a fixed nonzero vector in the real inner product space V .

What are the aspects and impacts of Air Conditioning Recharging?

y'' + y = te^it

Include the starting particular solution with unknown functions of t: A and B. Identify the system of equations to solve to find A' and B'. Write the integrals to solve to find A and B. Solve the integrals to find A and B. Write the particular solution that results from Variation of Parameters.

Use the Gauss-Jordan elimination method to solve the following system of linear equations. State clearly whether the system has a unique solution, infinitely many solutions, or no solutions. { ? + 2? = 9

? + ? = 1

3? − 2? = 9

Follow the steps bellow to construct a general solution to the equation:

y'' + y = 3sect -t²+1

a. find the general solution to the homogeneous version of the problem

b. find the particular solution to y'' + y = 3sect

c. find the particular solution to y'' + y = -t²+1

d. use part (a), (b), (c) to construc the general solution to the original given DE

Can you apply L'Hopital's rules to the following limit?

lim x approaches infinity (1+cos(x)) / sin(x)

true or false

Find the sum (n=5, to infinity) of the series (n² -n)/2ⁿ

h(t)=60t-t^4+1 represents the height of an object with respect to time.
what is the height of this object after t=5 sec?
find derivative using limits definition?
what is the velocity of the object at t=5 sec?

find the equation of the tangent line to h(t) that is perpendicular to g(t)=-1/40t-36.

Part A: Express the quadratic function in standard form (vertex form). ?(?) = 1 − 12? − 4? 2

Part B: Find the quotient and remainder using synthetic division. ?^4 + 2?^3 − 10? all over ? − 3

Part C: A stone is thrown upward from the top of a building. Its height (in feet) above the ground after t seconds is given by the function ℎ(?) = −16?^2 + 96? + 48. a. What maximum height does the stone reach? Find the maximum height algebraically.

b. How long does it take the stone to hit the ground? Give an exact value.

Suppose that a₁-12 and a_n+1 is a third of the value of a_n for all n=1,2,3,4,5.... natural numbers.

a) find the first foudn terms fo the sequence

b) find the formula for all values of the sequence

c) compute the exact value of the infinite sum