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Centre and radius of sphere and integration

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(See attached file for full problem description with proper equations)

Evaluate these:

1. Find dw/dx for the function given by w=xye^(xyz)

2. Find the center and radius of the sphere given by the equation
x^2 + y^2 + z^2 + 4x - 2y + 2z=10

3. The sum of $2000 is deposited in a savings account earning r percent interest compounded continuously. The amount A(r,t) after t years is given by A(r,t)= 2000e^(rt). Determine the amount in an account earning 8% interest for 5 years.

4. Integrate xydA where R is the region by y= sqrt(x), y=1/2x, x=2 and x=4
2 1-x
5. Evaluate (4-y)dydx
-1 0

2 sqrt(4-y^2)
6. Evaluate 0 0 (y+x)dxdy

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This solution provides assistance with the calculus problems given below.

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