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Calculus Questions
Verify the Divergence Theorem for the vector field F(x, y, z) = < y, x ,...
A rectangular storage container with an open top is to have a volume of 10 m3....
What is the solution to the initial value problem below? y′=7ex+7x3+x+3 y(0)=2
Infinity Sigma n=1 (pi^n/n!sqrt(n)) Does it converge or diverge
Find the volume of the solid bounded by the spheres x^2+y^2+z^2=1 and x^2+y^2+(z-1)^2=1 bu using spherical...
Suppose the material for the top and bottom costs b cents per square centimeter and the...
A study of a country's colleges and universities resulted in the demand equation q = 20,000...
The management of a factory finds that the maximum number of units a worker can produce...
10) What is the value of this prefix expression when read as an infix expression? Draw...
Use Stokes' Theorem to evaluate the surface integral ∬ G curl F ⋅ n d S...
Estimate the area under the graph of f(x)=x2+4x from x=2 to x=10 using 4 approximating rectangles...
How to solve with partial fraction decomposition?
1. Find the second derivative of : ? = 5?? (??(?)) 2. Find the second derivate...
By using method of variation of parameters the particular solution of the following differential equation y″+y=sec2(x)...
A wire is to be cut into two pieces. One piece will be bent into an...
Pat made the substitution x − 3 = 2sin t in an integral and integrated to obtain...
Determine where the graph of the function f(x) = 6x-√(4-x^2) is concave upward and where it...
Find the equations of the tangent and normal to the curve x2 + y2+3xy-11 = 0...
f(x)= (3500x-14700)^3 (x-230) When is it increasing or decreasing?
f (x) = x cos(x^2 ). Find f (21) (0). (21st Derivative x=0) Using Taylor Series.
Use logarithmic differentiation to find the derivative of y with respect to the given independent variable....
1. Find the y-intercept of the curve that passes through the point (5, 8) if, dy/dx...
How do you determine the sign of an infinite limit without a graphing calculator?
1- Use the definition of a Taylor series to find the first four nonzero terms of...
Identify a specific function f that has the following characteristics. Then draw it's graph. f(0)=3 f'(x)=-2...
3. Solve & graph the solution of the exponential growth model with the fixed per capita...
Use the given transformation to evaluate the integral. 3x2dA, R where R is the region bounded...
Find an approximation of the area of the region R under the graph of the function...
A Calculus instructor needs a model of a leaking tank for upcoming word problems. She decides...
Use Lagrange Multiplier to determine maximum and minimum. f(x,y)=(y^2)-7x^2 subject to (x^2)+(2y^2)=4
A closed three dimensional box is to be constructed in such a way that its volume...
2y′′+18y=0 y(0)=5 y′(0)=3 Solve I.V.P.
Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize f(x,...
you and a friend are riding your bikes to a restaurant that you think is east;...
1.) Calculate the consumers' surplus at the indicated unit price p for the demand equation. HINT...
Use linear approximation to find a linear representation for ? = √1 + 3? ?? ?...
1)Find the centroid of the region (Sketch the region, set up the integral. Locate the centroid...
for the following series state whether the divergence test applies either state that lim n-> infinity...
Consider the region bounded by y=2x and y=x^2. Rotate it about the Y-axis. Find the volume...
definite integral 0 to 7 of e^(x)sin(x)dx
1. Suppose you have a circular tank with a 3 meter diameter and 2 meter height...
Use Newton's method to find all solutions of the equation correct to six decimal places. (Enter...
Which functions fit the description? function 1: f(x)=x^2 + 12. function 2: f(x)= −e^x^2 - 1....
2. Find the solution to the following IVP: 2y'' +2y' -2y = 6x^2 - 4x -1...
Find the second derivative; y” ; for ???? − ???? = ?
A particle moves according to a law of motion s = f(t), t ≥ 0, where...
A 30 foot long chain weighing 90 pounds hangs over the edge of a 40-ft tall...
For the function , (1)/(3)x^(3)-3x^(2)+8x+11 1)at x=, f(x) attains a local maximum value of f(x) 2)at...
Draw a diagram and solve: What is the exact area of the biggest isosceles triangle you...
find a function whose graph has the given asymptotes x=-8, x=3, and y=8 a) f(x)= 8x^2...
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter...
What is the general solution of x(k) = et? x(k) means the kth derivative of x....
Infinity Sigma n=1 (n+1 / n^7/3 + sqrt n) Does this series converge or diverge?
4. Draw a diagram and solve: You have 64 square feet of cardboard which you want...
Find constants a and b such that the function T(x,y) = x2+2ax+y2-by has a local maximum...
(true or false), csc(x), cot(x), and tan(x) have the same vertical asymptotes .
Use a 2nd order Taylor polynomial centered at x = 4 to approximate √4.001 You can...
1. Find the Area of the region bounded by the graphs of y=2x and y=x2-4x ...
Find the equation for the tangent line to the curve x2y +x3 = 1 at the...
A power house cable runs from point P to a factory at point F located on...
Apply Newton's Method to approximate the x-value(s) of the indicated point(s) of intersection of the two...
Find the half range cosine Fourier series expansion of the function f(x) = x + 3,...
A picture 7 feet high is placed on a wall with its base 9 feet above...
Suppose Aaron is pumping water into tank, shaped like an inverted circular cone, at a rate...
Which of the following differential equations are separable? (Select all that apply.) A. ????=??−?d B. ????=−3?...
True or False，and explanation If X is bell-shaped and symmetric, then Chebyshev's rule does not apply.
Q6. Find the moment of inertia Iy for the circular lamina x + y ≤ R...
Q7. Evaluate ∫∫ G(r)dA where G(x, y, z) = arctan(y/x) and S is given by z...
Suppose the demand and supply functions for a product are P= 2800-8q-1/3q^2 and p = 400+2q,...
Q8. Let G be the cylindrical solid bounded by x2 + y2 = 9, the xy-plane,...
The red cell volume RCV (in milliliters) for males is related to surface area S (in...
Sketch the curve of the graph of y = (the square root of (1-x^2)) / x...
related rates ? water flows into a giant basin at a constant rate of 7 cubic...
Find the intervals of increase and decrease as well as the local extrema for the function...
Solve the following differential equation by Laplace transforms. The function is subject to the given conditions....
Sketch the region enclosed by the given curves, decide whether to integrate with respect to x...
Suppose a Cobb-Douglas Production function is given by the following: P(L, K) = (50L^(0.5))(K^(0.5)) where L...
Notice that ?y/?x = (3y+2x)/(x+y) is not separable. However, we can solve the equation with the...
find the interval where the function is increasing and decreasing f(x) =(x-8)^2/3 a) decreasing (8, infinity)...
Please integerate sin^4(t) using Euler's formula and explain every single step, assume I have no prior...
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