Purchase Solution

Solve: Multivariate Calculus

Not what you're looking for?

Ask Custom Question

Please see the attached file for full problem description.

(a) where R is the region in the first quadrant which lies inside the circle x^2 + y^2 = 2x and outside the circle x^2 + y^2 = 1.

(b) If f(x,y) = x/y and h(x,y) = (1/2)x^2 - 4y find the rate of change of f(x,y) at the point (2, -1) in the direction in which h(x,y) is increasing most rapidly.

Purchase this Solution

Solution Summary

This solution provides a very detailed, step by step response demonstrating how to approach a problem with a double integral, and another problem dealing with the rate of change. An explanation accompanies each step. A pdf. file is attached which contains the complete solution.

Solution Preview

(a) Whenever you see a double integral involving (x^2 + y^2) try transforming using polar coordinates to see if it simplifies. Remember the relations for polar transformations:

x = r cos theta y=rsin theta
x^2+y^2 = r^2
and the Jacobian gives
dxdy = r dr dtheta

Now the region of interest R is the segment in the 1st quadrant bounded by the circles with radii 1 and sqrt(2*pi). In polar coordinates since we are restricted to the first quadrant we have 0 < theta < pi/2. For the r variable we must restrict ...

Purchase this Solution

Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts