Average distance from a point on a disk.

Please see the attached file for the fully formatted problem. Show that the average distance of a point of a disk with radius a is...

Surface area of the part of a sphere that is inside a Cylinder

Please see the attached file for the fully formatted problem.

Volume enclosed by a surface.

Show that the volume enclosed by the surface ___ is equal to ___. Please see the attachment.

Find where a Line Intersects a Circle

Determine the points where the line intersects the circle.. 4x+3y=24 x^2+y^2=25

8 calculus problems

Please answer eight (8) calculus problems. Please show as much works as possible for every problem. The problems are posted in the following website: http://www.netprofitspro.com/math.html

Differentiation using the product rule and the chain rule with the exponential function

Find the derivative of the function y=x^2e^(3x) See Attachment for a cleaner version of the question.

Triple Integrals : Finding Volume of Solids with Boundaries

1) Evaluate the triple integral e^(1-(x^2)-(y^2)) dxdydz with T the solid enclosed by z=0 and z= 4-(x^2)-(y^2) 2) Find the volume of the solid bounded above and below by the cone (z^2) = (x^2) + (y^2), and the side by y=0 and y= square root(4-(x^2)-(z^2))

This problem involves evaluating an indefinite integral using the substitution rule.

Evaluate the following indefinite integral. int[(x^a)sqrt(r+tx^(a+1))]dx, (t not=0, a not=-1). (See attachment)

Fibonacci sequence in closed form

Prove that Fn can be expressed by: Fn=[(a^n-b^n)/(a-b)] for n=1,2,3... ~: Set Gn=[(a^n-b^n)/(a-b)] and show that Gn satisfies the recurrence formula {G(n+1) = Gn + G(n-1) for n=2,3,4...} and don't forget that a and b satisfy the equation x^2-x-1=0. a and b are the roots of x^2-x-1=0, which are (1+sqrt5)/2 and (1-sqrt5)/2 ...continues

Power & Taylor Series of Fibonacci

Interval of Convergence of a power series a. Consider the Power series sum of series from n=1 to infinity of FnX^n. Use the ratio test to determine the open interval on which the pwr series converges. b. Show that the Taylor series of the Fcn f(x) = x/(1-x-x^2) about x=0 is given by: x/(1-x-x^2) = sum of series at ...continues