194 Answered Questions for the topic Calculus 3

06/26/16

triple intergral
An engine part is a solid S in the shape of an Egyptian-type pyramid having height 2 and a square base with diagonal D of length 2. Inside the engine it rotates about D. Set up an iterated integral... more
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06/26/16

calculate curl F
Calculate div F and curl F for F = rn (xi + yj). (simplify the differentiation by using rx=x/r, ry=y/r) For which value(s) of n is div F=0? For which value(s) of n is curl F=0?
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06/25/16

greens thorem in the normal form.
verify green's theorem in the normal form by calculating both sides and showing they are equal if F= x2i + xyj, and C is the square with opposite vertices at (0,0) and (1,1)
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06/24/16

max and min of directed line segment
Let F= i + j.  How would you place a directed line segment C of length one so that the value of ∫cF*dr would be a. a maximum b. a minimum c. zero d. what would the max and min values of the... more
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06/23/16

gradient fields and exact differentials
A. let f(x,y)= xexy, and C be the path y=1/x from (1,1) to (0,∞)       1. calculate F=∇f       2. Calculate the integral ∫cF*dr           - directly          - by using the fundamental theorem... more
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Calculus 3

05/23/16

a sphere is centered on the origin and contains point (1,-1,1) on it surface. what is the equation of this sphere
I think I know how to do it, but I am getting a radius of 1, but my solution says the radius is 3 
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Calculus 3 Calculus

05/01/16

Find the area of the region R bounded by the curve r = 6cos 0
Find the area of the region R bounded by the curve r = 6cos 0
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Calculus 3

04/25/16

Let R be the region in the plane bounded by the lines y = x^2, x = 0, and y = 4. Evaluate the double integral xe^(y^2) dA
for the limits of integration I got x^2 to 4 and 0 to 2.
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Calculus 3

04/20/16

given the function f(x,y)=3x2-2xy+4y2 in which direction does the function drop most rapidly at the point p (1,1) and calculate the derivative of the function
given the function f(x,y)=3x2-2xy+4y2in which direction does the function drop most rapidly at the point p (1,1) and calculate the derivative of the function in that direction
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Calculus 3 Volume

04/19/16

Finding the volume of a region
Find the volume of the region inside the sphere x2+y2+z2=1 and outside the cylinder x2+y2=1/4. How would I set this up using the a triple integral?
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Calculus 3 Volume

04/13/16

Find volume of Solid
Find the volume of the solid bounded by x2+2y2=2, z=0, and x+y+2z=2
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Calculus 3 Volume

04/13/16

Finding the volume under graph
Find the volume under the graph of f between the planes x=a,x=b,y=c,y=d. f(x,y)=x3+y2+2 ; a=-1,b=1,c=1,d=3.
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Calculus 3 Arc Length

04/07/16

Find the arc length
Find the arc length of the curve c(t)=(t3/2,cos(2t),sin(2t)), 0<=t<=1.
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04/07/16

Finding maximum on curve
Find the maximum of f(x,y)=xy on the constraint curve (x+1)2+y2=1.
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Calculus 3 Calculus

04/06/16

Critical point, Local max or min?
Let z=(x2+y2)sin(2x+y). Show that (0,0 is a critical point. Is it a local max or min? 
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Calculus 3

04/03/16

find the point on the plane
find the point on the plane 20x+15y+12z = 120 that is closest to the sphere x^2+y^2+z^2=1
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Calculus 3 Volume

03/18/16

Help with volume -calculus 3
A parcel delivery service requires that the dimensions of a rectangular box be such that the length plus twice the width plus twice the height be no more than 108 inches (L+2W+2H <= 108). What... more
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03/18/16

Given the vectors below, carry out the operation.
Given the vectors below, carry out the operation.     u=(4, -2) v=(-4, 6 )   2u+3v    
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03/18/16

Plot the curve below and describe the picture in words.
Plot the curve below and describe the picture in words.       r=3 sin4θ
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03/18/16

What test would you use to determine whether the series below converges or diverges?
    ∑_(k=1)^∞ 1/k^(1+n) , n>0
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03/18/16

Using the disk method, find the volume of the solid generated by revolving about the x-axis the area bounded by the curves below.
Using the disk method, find the volume of the solid generated by revolving about the x-axis the area bounded by the curves below.   x=0 y=0 y=−2x+2
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03/18/16

Find the domain and the range of the function below.
Find the domain and the range of the function below.   g(y)=1/(y−2)
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03/17/16

Find a) the angle between u and v, b) projv u and c) scalv u. Recall that a ? b = |a||b| cos ?.
Find a) the angle between u and v, b) projv u and c) scalv u. Recall that a ? b = |a||b| cos θ.     u=-3i+4k v=-4i+j+5k
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03/17/16

The Cosine function is a Taylor series. Expand the series to 4 terms and use the result to approximate Cos (2p). How does the approximation compare to the actua
The Cosine function is a Taylor series. Expand the series to 4 terms and use the result to approximate Cos (2π). How does the approximation compare to the actual result? What would you need to get... more
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03/17/16

Using the disk method, find the volume of the solid generated by revolving about the x-axis the area bounded by the curves below.
Using the disk method, find the volume of the solid generated by revolving about the x-axis the area bounded by the curves below.     x=0 y=0 y=-2+2
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