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Calculus
Find the volume of the solid generated by rotating the region bounded by the curves y=0, y=x^2+x, and x=2 about the y-axis
Calculus
Find dy/dx at (1,2) of the function xy²-y-4x²+2=0
Calculus
Show that the function
1
2 2
2
tan ( ) xy
z
x y
−
=
−
satisfy Laplace equation.
1
2 2
2
tan ( ) xy
z
x y
−
=
−
satisfy Laplace equation.
Calculus
Find the mass and center of mass of a triangular lamina with vertices
(0, 0), (1, 0)
and
(0, 2)
if the density function is p(x,y)=1+x+y
(0, 0), (1, 0)
and
(0, 2)
if the density function is p(x,y)=1+x+y
Calculus
Find the volume of the solid that results when the area of the region enclosed by y=x^3, x=-1, and x=1 is rotated about the x-axis
Calculus
A 30-foot length of steel chain weighing 12 pounds per foot is hanging from the top of a building.
how many foot-pounds of work are required to pull half of the chain to the top?
A: 2080ft-lbs B: 1250ft-lbs C:4050ft-lbs D:5200ft-lbs
Calculus
Multiple choice: Find the volume of the solid that results when the region enclosed by the graphs of y=x^2 and y=2x is rotated about the x-axis
A:4/15 B:1/6 C:2pi/3 D:64pi/15
A:4/15 B:1/6 C:2pi/3 D:64pi/15
Calculus
Three people live on the unit sphere and are going to walk from North
Pole (0,0,1) to the South Pole (0,0,−1). The first person walks along the
arc of a great circle that lies in on the coordinate planes. The second
person walks along an arc of a great circle that does not lie in one of the
coordinate planes, and the third walks along a curve that spirals once
around the sphere. Find the parametric equations that describe possible
paths for each person.
Calculus
Using the first principle, find the derivative of the function f (x) = 1 . (Show all workings and √x+1
state clearly, any theorem used)
state clearly, any theorem used)
Calculus
Find the Fourier series for the function
f(x) = (x-x)^2,-L < x < L
f(x) = (x-x)^2,-L < x < L
