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Calculus Questions
The marginal revenue in USD for business A for selling x units per day of some...
Air is being pumped into a spherical balloon so that its volume increases at a rate...
Find an equation of the tangent plane to z=32-3(x^2)-4(y^2) at the point (2,1,16)
find the curvature of the curve r(t). r(t) = (8+8cos5t)i -(4+8sin5t)j + 8k
A storage company must design a large rectangular container with a square base. The volume is...
18 a.) A rocket is launched at an angle of 75̊ with the ground and an...
12. a.) If u = (0, 2, 3) and v = (1, 3, -1), find the...
Evaluate the limit. lim ?→0 (1 + arctan(?ln8)) 1/ 3?
Water is being poured into a cone-shaped container with radius 4 inches, and height 4 inches....
For each cost function (given in dollars), find the cost, average cost, and marginal cost at...
Sketch the region enclosed by y = sin ( π /3 x ) and y =(...
There is an open-topped box that will have 5 sides.. The box to contain a volume...
Consider the following problem: A farmer with 650 ft of fencing wants to enclose a rectangular...
x^5 +x^3 +x +1=0 use the IVT and Rolle's theorem to prove that the equation has...
A rectangular box is to have a square base and a volume of 20 ft3. If...
Assuming U represents the universal set and S represents any set, which of the following is...
The revenue from the sale of x blankets with arms is given by R(x)=28x−0.2x^2 dollars. The...
An object is launched upward from a platform so that its height (in feet) above the...
2. Use integration in cylindrical coordinates in order to compute the volume of: U = {(x,...
Evaluate the integral: ∫ 21/ x 2 √ x 2 + 49 d x
find Taylor sequence at a=-1 for f(x)=x4+2x3+x-4 under assumption that f has a power series expansion....
Select "True" or "False" for the sentence or statement. 1. All relative extrema occur at first...
A triangular plate with base 6 m and height 2 m is submerged vertically in water...
Find the maximum and the minimum speeds of a particle whose motion is described by the...
let f(x)=xcosx + 2 tan x. Find f"(x)
4. Given L {sinh (-4t)} = -(4/ (s2 -16)), find L{ t sinh (-4t) } 5....
please don't answer unless you can do all parts, circle answer and show work please part...
find the volume of the solid obtained by rotating the region bounded by rotating the region...
1- A spherical balloon is inflated so that its volume is increasing at the rate of...
Consider the region R between the x-axis and the curve y = ((x √ x) /...
Find the linear approximation of the function f(x, y, z) = sqrt x2 + y2 +...
1. Calculate the total differential for the given function. G(x,y) = e^5x ·ln(xy + 1) 2....
A box is contructed out of two different types of metal. The metal for the top...
dy/dx = ysin(4x)/(y-4) a) Find region of xy plane where the d.e has a unique solution...
How do you find the area of the surface x2+y2-z=0 between z=1 and z=3 ?
For what values of is the angle between the vectors i+2j-2k and 4i+cj-3k equal to 48...
A university is trying to determine what price to charge for tickets to football games. At...
A rock is dropped from a height of 64 ft. It is determined that its height...
Find the cone with the largest volume using 25 square units of material.(yes the cone has...
Optimal Chapter-Flight Fare If exactly 210 people sign up for a charter flight, Leisure World Travel...
The number x of printer cartridges that a store will sell per week and their price...
Suppose that f(t)=t^2+1-5 (a) What is the average rate of change of f(t) over the interval...
find the tangent plane to the surface x^2 + 2xy + z^3 = 4 at point...
A covered mug of coffee originally at 190 degrees Fahrenheit, if left for t hours in...
Chapter 8, Section 8.6, Question 003 Use Lagrange multipliers to find the maximum and minimum values...
Find the area of the region in the ?? x y -plane bounded above by the...
When Pilar is 12, her grandparents begin placing a continuous stream of $2,000 per year into...
A radioactive element of 100g has a 1/2 life of 10 days. a) find the rate...
Given the function f(x, y) = xe2xy, estimate f(1.1,-0.1) using the linearization of f at the...
Find the exact length of the curve. Part A x = 4 + 12t2, y =...
Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare...
7. Suppose p(x) = a0 + a1x + a 2 x 2 + · · ·...
3. Find the volume of the solid obtained by revolving the region below y = 4...
Consider the function f(x)=−8x−(2888/x) on the interval [11,20]. Find the absolute extrema for the function on...
Consider the function g(x) = |3x + 4|. (a) Is the function differentiable at x =...
The amount spent on cable TV per person per year from 2000 through 2015 can be...
Two spacecraft are following paths in space given by r1=〈sin(t),t,t^2〉 and r2=〈cos(t),1−t,t^3〉. If the temperature for...
9) Use whatever test you like to classify the local maxima and minima of the following...
Consider the differential equation: 66t^2y''+12t(t-11)y'-12(t-11)y=5t^3, . You can verify that y1 = 5t and y2 =...
Find the local maximum and minimum values and saddle point(s) of the function. If you have...
A woman is constructing a rectangular pen surrounded by fence with four additional fences across its...
A barrel of heating oil is selling for $200, and its price is increasing by $1.75...
Consider the differential equation y'=-x-y Use Euler's method deltax=.1 to estimate y when x=0.2 for the...
A farmer needs to build a rectangular pen with one side bordered by a river (that...
f(x)=((2x+4)(5x+2))/((7x+8)(7x+6)) 1. Find the vertical asymptote(s). If there is more than one vertical asymptote give a...
Suppose z is implicitly implicitly defined by the equation: F(x, y, z) = 4x^ −1 −...
F(x) = ( (x+3)/(x+1) )2 find the domain of F and any critical numbers, horizontal asymptotes,...
Suppose a business can sell x gadgets for p = 250 - 0.01x dollars apiece, and...
Consider the parametric curve defined by x = 3t − t^3 , y = 3t^2 ....
Consider the following system of equations: 2x1 + 8x2 = 2 x1 + x2 = 4...
Consider the differential equation. Find the solution y(0) = 2. dy/dt = 4t/2yt^2 + 2t^2 +...
(10 marks) Analyze and sketch the curve y = x3 − 6x2 + 9x. A full...
Differentiate 4x . log 2 5x ( 2 is the base of log) 9x/(x5+2x+3)
Effect of Price on Supply of Eggs Suppose the wholesale price of a certain brand of...
Question 1 [15 marks] Provide all necessary steps to find the limit of the following functions:...
Let f(x,y) = xe^sin(x^2y+xy^2) /(x^2 + x^2y^2 + y^4)^3 . Compute ∂f ∂x (√2,0) pointwise.
Explain whether the following integrals converge or not. If the integral converges, find the value. If...
Let F (x1, x2) = ln(1 + 4x1 + 7x2 + 6x1x2), x = (x1, x2)...
1.) A farmer wants to fence in a rectangular plot of land adjacent to the north...
2. (b) A ball is thrown in the upward direction is to reach a maximum height...
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