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Calculus Questions
Determine whether the series is convergent or divergent. If it is convergent, find its sum. (a)...
The curve r(t) = <sin(t),sin(t+sin(t))> intersects itself at (0, 0). Find the acute angle (in radians)...
Use the Laplace transform to solve the given initial-value problem. y'' + y = f(t), y(0)...
dentify the absolute minimum and absolute maximum values of the function f(x)=x3−12x2−27x+22 f ( x )...
An object weighing 300 pounds is suspended from the top of a building by a cable...
Consider the plane region R bounded by the curve y = x − x 2 and...
z= f(x,y) = xy-2x-3y+6 has one critical point (x,y,z). Please find it 2) f(xx)= 3) f(xy)=
How long will it take an investment of $2000 to double if the investment earns interest...
The linear density ρ in a rod 5 m long is 9/sqr(x+4) kg/m, where x is measured...
Find the producers' surplus for a product if the supply function is given by S(x)=0.19e0.1xS(x)=0.19e0.1x and...
Use Stokes’ Theorem to calculate the flux of the curl of the vector field F =...
Let S be the portion of the surface z=cos(y) with 0≤x≤4 and -π≤y≤π. Find the flux...
A company manufactures microchips. Use the revenue function R(x) = x(75-3x) and the cost function C(x)...
Solve the system dx/dt = [ row 1: -5 -1 row 2: 1 -5] x with...
Please write detailed notes on the following topics with examples: integration techniques, differential equations, parametric equations,...
Find the minimum distance from the origin to the parabola y=5-x^2
On the parametric curve (x(t), y(t)) = (t − t^2 , t^2 + 3t) pictured below,...
If the infinite curve y=e-x, x>/=0 is rotated about the x-axis, find the area of the...
Which of the following statements is true? a) The geometric series Σ∞n=1 r^n is always convergent....
Use spherical coordinates to calculate the triple integral of ?(?,?,?)=1/(?^2+?^2+?^2) over the region 6 ≤ ?^2+?^2+?^2...
Find the radius of convergence, R, of the series. ∞ (x − 2)n /n 3n n...
At Kirk’s Audio Emporium, 10% of the customers buy an extended warranty for the items. For...
Find the centroid of the region bounded by the curves: y = 8 - x2 ,...
Calculate all four second-order partial derivatives for the function f(x,y)=3+6x2y2 ?
A plane flying with a constant speed of 14 km/min passes over a ground radar station...
Use substitution to find a Taylor series representations for the following functions. You should not use...
After an appropriate trig substitution, the integral x^2sqrt(4-x^2) dx is equivalent to which of the following?
A farmer wants to fence in a rectangular plot of land adjacent to the north wall...
Find the flux of the curl of field F through the shell S. F = -4z...
A tank is filled with liquid of density 1000 [kg/m3 ]. Its shape is obtained by...
A graphing calculator is recommended. Use Newton's method to find all solutions of the equation correct...
Evaluate the integral by changing to cylindrical coordinates. 5 −5 25 − y2 − 25 −...
Consider the polar curve ? = cos(?) + 1. To find the area enclosed by the...
F(x, y) = yi + xj (a) Show F is conservative Given your answer in (a)...
Consider plane P: 4x -y + 2z = 8, line: <x, y, z> = <1+t, -1+2t,...
Company MNO generates between 10800 and 14500 million dollars revenue per year. Suppose that the company's...
(1 point) This problem is similar to one in your textbook. Suppose that a company needs...
find f(x) f"(x) = x^2 f(1) = 0 f(2) = 0
(1 point) Solve the separable differential equation ?′(?)=√(4y(x)+32), and find the particular solution satisfying the initial...
Let F = < 2?, −2? > and ?, the region bounded by ? = sin...
4) Consider the polar curve r=e2theta a) Find the parametric equations x = f(θ), y =...
differential equation
A particle moves in a straight line with the given velocity ?(?)=9cos(?) (in m/s). Find the...
A tank contains 1000 L of pure water. Brine that contains 0.05 kg of salt per...
Find the absolute maximum and absolute minimum values of f(x,y) = x^2 + 2y^2 − 2x...
A tank initally contains 10 liters of blue paint. Then red paint enters the tank at...
Solve the IVP x''+ax=b+e-ct, x(0)=x'(0)=0, a, b, c all positive parameters. Does your solution approach a...
Let f(x,y) = 3x^2y − 2y^2 − 3x^2 − 8y + 2. (i) Find the stationary...
1. Evaluate the definite integral given below. ∫(from 0 to π/3) (2sin(x)+3cos(x)) dx 2. Given F(x)...
Find the surface area of the portion of the plane 3x+2y+z=6 that lies in the first...
D(x) is the price, in dollars per unit, that consumers are willing to pay for x...
Consider a function ?(?,?) whose graph is the bottom half of a sphere radius 10 centered...
A keyboarder's speed over a 55-min interval is given by the following function, where Upper W...
Consider the region R bounded by y = sinx, y = −sinx , from x =...
Polar Coordinate Problems 1. Identify when the function decreases when changing r2sin (??) = a(−?)b to...
Evaluate the triple integrals E y2 dV, where E is the solid hemisphere x2 + y2...
Consider the Bernoulli equation ?′ + (1/x)? = ?33 a. Convert to a first order linear...
1) Find the volume of the solid formed by rotating the region enclosed by y=e^(5x)+2, y=0,...
Use the method of undetermined coefficients to solve y′′−3y′+2y=30sin(x)+ 12e−x+ 2 Could you go step by...
Daily crude oil production by Pemex, Mexico’s national oil company, for 2008-2013 could be approximated by...
In a city with a population of 500,000, the rate of change of the number of...
The average cost function for the weekly manufacture of retro portable CD players is given by...
Please answer ASAP Find the volume of the solid by subtracting two volumes, the solid enclosed...
1. You own a hamburger franchise and are planning to shut down operations for the day,...
A university student center sells 1,600 cups of coffee per day at a price of $2.40....
A plane flying horizontally at an altitude of 5 mi and a speed of 470 mi/h...
find the integral of f(x,y,z)=x over the region x^2+y^2=1 and x^2+y^2=9 above the xy plane and...
If ?(?) = 20000 + 400? − 5.2?^2 + .002??^3 is the cost function and ?(?)...
Determine whether the following series converges or diverges:∞∑n=1 ln(1 +1/n).
Calculate work done by particle by force field along the x axis from (-2,0) to (2,0)...
prove the identity arcsin [(x-1)/(x+1)]=2arctan(square root x)-pi/2 for x greater than or equal to 0 using...
Find the area of the region bounded by the graphs: y=x^2-4 y=x^4-4x^2 I set the equations...
Please show all work Find and classify each critical point (as relative maximum, relative minimum, or...
The weekly cost (in dollars) of producing x compact discs is given by C(x) = 2000...
find the equatiion of the tangent line to 4x^2+2xy-y^3 at the point (1,2)
find the rate of change of total revenue, cost, and profit with respect to time. Assume...
(1 point) Let SS be the part of the plane 2x+4y+z=1 which lies in the first...
How many terms of the series n=2 to infinity 12/(6n ln(n)^2) would you need to approximate...
Until recently, the hamburgers at the city sports arena cost $4.60 each. The concessionaire sold an...
Do the following sequences converge or diverge? If it converges, find its limit. a) an =...
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