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In 2004, an art collector paid $56,738,000 for a particular painting. The same painting sold for...
For the following exercises, find the length of the curve over the given interval. r=8+8cosθ on...
. a. [2] Compute the divergence of vector field F = x 3y 2 i +...
The line l1 has the direction vector h1,0,−1i and passes through the point (0,−1,−1). The line...
Suppose r(t) = t2i + (t3 −t)j + (t−1)2k is the position vector of a moving...
At noon, ship A is 40 nautical miles due west of ship B. Ship A is...
Consider the sum of double integrals Z1 1/√2Zx √1−x2 xy dy dx +Z√2 1 Zx 0...
6. Let R be the tetrahedron in the first octant bounded by the coordinate planes and...
Find the work done by the force field F(x,y,z) = yz i + xz j +...
6. Compute for the arc length of y = 1/ 2 x + 3 from x...
A conical tank of diameter 6 m and height 10 m is filled with water. Compute...
Integral of (2x - 1)^3 dx
a 10 ft long ladder is leaning against a vertical wall.the top of the ladder is...
A spherical tank of radius 4 ft is being filled with water at the hole in...
Denote by a the sum of the 5th and 6th digits of your student number. Solve...
Cody manages a store that sells video games. Each MX300 takes 2 hours to create the...
The sum of two positive numbers is 32. What js the smallest possible value of the...
A solid has a circular base of radius 1. Its parallel cross-sections perpendicular to the base...
Suppose you deposit $7000 at 7% interest compounded continuously. Find the average value of your account...
In what direction does f(x,y)=ln(7x^2+8y^2) increase most rapidly at (4,5)? Answer with a unit vector
A dangerous radioactive material is to be used in a medical procedure on patient Z. •...
A regular page is to contain 36 square inches of print. The margins on each side...
1. A tire manufacturer estimates that q thousand radial tires will be purchase by wholesalers when...
Find the maximum volume that a rectangular box can have if the length is twice the...
Sketch the region enclosed by the given curves. y = |9x|, y = x2 − 10...
Find the equation of the line tangent to the curve at the point (-5,2) xy^3+x^2=x-5y
An object starts from rest at point P(1,2,0)P(1,2,0) and moves with an acceleration of a(t)=j+2k,a(t)=j+2k, where...
Find the antiderivative of r'(t)=cos(2t)i−2sintj+11+t2kr'(t)=cos(2t)i−2sintj+11+t2k that satisfies the initial condition r(0)=3i−2j+k.
f(x) = − cos(x^2 ) + 2 sin(x) [1,3.5] 1) find f'(x) and the roots on...
1. Solve the optimization problem. If the price charged for a candy bar is p(x) cents,...
Find the absolute maximum and minimum, if either exists, for the function on the indicated interval....
Problem 6. Use Euler’s Method to approximate the particular solution of this initial value problem (IVP):...
Proof of the Mean Value theorm with a short explanation?
A fence must be built in a large field to enclose a rectangular area of 18,225...
Suppose we take the interval [−4,8] and divide it into 4 equal subintervals. Find the width...
Set up a double integral in rectangular coordinates for the volume bounded by the cylinders x^2+y^2=1...
Cost, revenue, and profit are in dollars and x is the number of units. A firm...
A particle is moving with the given data. Find the position of the particle. a(t) =...
a) Find two numbers whose sum is a maximum and whose product is 125. What is...
Suppose you wish to make a special cylindrical can holding a volume of 1 liter. If...
1. A potato is removed from an oven with the temperature 350 degrees F. It is...
Find the arc length of the given curve on the specified interval, (t, t, t2), for...
1. Convert y^2 =9x into to the full polar coordinates. Show work. 2. Solve the differential...
Find the exact length of the curve y=(x^3)/3 + 1/(4x) for 2≤x≤3 Conslder the curve deflned...
A function f, a closed interval [a, b], and a number of equally spaced subintervals n...
12. Find the absolute maximum and minimum of the function p(x)= 2x2-7x+9 over the interval [-1,3]....
1. Write a geometric series with a starting index of n = 0 which has a...
Find the shortest distance between line L1: x = 1 + 2t, y = 3 -...
What can you say about the curvature of the curve y = f(x) at the point...
1. A rectangular hole is to be cut in a wall for a vent. If the...
11. Determine the vertical and horizontal asymptotes (if any) of the following function: f(x)= 5x2-3x+5/2x2+9x-5. 13....
Find the volume of the solid generated by revolving the plane region bounded by the graphs...
A rectangle with side lengths given in feet is located in the first quadrant of the...
Consider the following function. f(x) = ln(1 + 2x), a = 1, n = 3, 0.8 ≤ x ≤...
The method of Lagrange multipliers assumes that the extreme values exist, but that is not always...
Use the Left and Right Riemann Sums with 100 rectangles to estimate the (signed) area under...
Fidn the area of the surface of the rotating curve y=(10-x)^1/2 from 0<y<5 about the x-axis....
Let f(x)=x^2 Find the first coordinate of the intersection point of the two tangent lines of...
Brandon is on one side of a river that is 80 m wide and wants to...
A manufacturer estimates that its product can be produced at a total cost of C(x) =...
Let C be the curve parametrized by r(t)=(t2+2)i+(1+t)j+2t^2k, with 0≤t≤. Consider the conservative vector field F=yz2i+xz2j+2xyzk,...
Solve the initial-value problem for linear differential equation y'' + 4y' + 8y = sinx; y(0)...
12. Revenue from sales of a popular soft drink are approximated by R(t) = 4 −...
Evaluate the following integral: ∫3x (divided by)[(x(square)2+10x+30)]dx
1.A lemonade stands makes a profit of ?(?)=0.18? −44.82 dollars when selling ? units of lemonade...
In 1990 (t = 0), the world use of natural gas was 79413 billion cubic feet,...
Is the function continuous on (-infinity, infinity)? Explain. f(x) = cos x; if x<0 0; if...
Find the volume of the solid of revolution obtained by rotating the region bounded y=sqrtx and...
Let b(t) represent the population of bunnies on Greentree Island t weeks after the population was...
A furniture company determines that its marginal cost function for producing x tables is estimated by...
Find the equation for the tangent plane to the surface xy + yz + zx =...
A piece of wire of length 6161 is cut, and the resulting two pieces are formed...
I need to find the equations of the tangents to the ellipse 4x^2 + y^2 =...
Find the point P on the line yequals=44x that is closest to the point left parenthesis...
Find the directional derivative of the function at the given point in the direction of the...
The attendance (# of people) that attend a certain theater when the ticket price is $xis...
A television camera is positioned 4000 ft from the base of a rocket launching pad. The...
(1 point) Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(7,0,0),(0,10,0),(0,0,6).
find the taylor series for f(x)=1/(4x-1) at a=1
Find the shortest distance between the point (1, 4, 2) and the paraboloid described by z...
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