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Evaluate the following integral by first converting to an integral in polar coordinates.

0

2


4

y
2


4

y
2
x
2
d
x
d
y
∫−20∫−4−y24−y2x2dxdy
Use Weierstrass’ M-Test to prove that the series ∑(x^nXn^2)

n=1

n converges uniformly in x
the interval .
(0,1/5)
Use Weierstrass’ M-Test to prove that the series ∑(x^nXn^2)

n=1

n converges uniformly in x
the interval .
5
1
,0

[img]https://upload.cc/i1/2020/04/20/RAD7Mo.jpg[/img]


question is in picture,R=4
Find the indefinite integral of the following functions
Y= 3t^2+2e^3t+1/t+ cos 3t
Y=x/2+3x^2

Show your complete solution.


1. Use Lagrange Multiplier to determine the dimensions of a rectangular box, open at the top, having a volume of 32 cubic feet and requiring the least amount of material for its construction.


Find the sum of the x and y intercept of any tangent line to the curve √x + √y = √k
[img]https://upload.cc/i1/2020/04/18/6EeNfM.jpg[/img]


question in photo,R=4
Integrated ×^2+×+5/(×^2+4)(×+1) dx.
Integration by part
two boat each move a velocity v relative to the water and both cross a river of breadth a running with uniform velocity V.they start together one boat crossing by shortest path and the otherin shortest time.find the difference between the time of arrival.
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