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.

describe projection on the x-y plane ( center, radius)

describe projection on the x-y plane ( center, radius)

Set up triple integral for volume of cone.

Please see the attached file for the fully formatted problems. Set up triple integral for volume of cone, do not evaluate.

Sketch region and setup double integral.

Please see the attached file for the fully formatted problems. Sketch region and setup double integral.

Partial derivatives

The heat transfer in a semi-infinite rod can be described by the following PARTIAL differential equation: ∂u/∂t = (c^2)∂^2u/∂x^2 where t is the time, x distance from the beginning of the rod and c is the material constant. Function u(t,x) represents the temperature at the given time t and p ...continues

domain and range of a function

Describe the domain and range of the function. Represent the function graphically. f(x,y) = ln(4-x-y)

Level curves

Describe the level curves of the function. Sketch the level curves for the given values of c. f(x,y) = x^2 + 2y^2, c = 0,1,2,3,4

Gradients

A metal plate is located in an xy-plane such that the temperature T at (x,y) is inversely proportional to the distance from the origin, and the temperature at point P(3,4) is 100 (i.e. the temperature at any point (x,y) is described by the function T(x,y) = 500/(x^2 + y^2)^1/2 a) in what direction does ...continues