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

Set up integral for surface area.

Please see the attached file for the fully formatted problems. Use the formulas to set up an integral for the surface area of the first octant portion of the sphere p=a, do not evaluate. See attachment

Sketch the curve and set up double integral for bounded area.

Please see the attached file for the fully formatted problems. Sketch the curve r = 5 - 3cos(theta) and set up double integral for bounded area in the third quadrant.