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.

Double integrals

1. Evaluate the double integral e^(x^2 + 4y^2)with "gamma" the region enclosed by the ellipse ((x^2)/4 ) + (y^2) = 1 2. Evaluate the line integral of h(x,y) = (x^2 + y^2)i + (e^y)j over the closed curve C composed by the upper half of the unit circle and the x axis and traverse clockwise

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

Chain rule

You are given the function w=yz/x, where x=θ^2, y=r+θ and z=r-θ. Find ∂w/∂θ. a) using the appropriate chain rule b) converting w to a function of r,θ before differentiating. Which of the above is quicker?

Analysis/total differentials

Evaluate f(1,2) and f(1.05, 2.1) for the function ƒ(x,y)=x/y. a) calculate Δz b) use the total differential dz to approximate Δz