Calculus Answers

Find extreme values f(x,y)= 3xy on 2x+y=8

Find the extreme values of f(x,y)=x+y^2 on the surface 2x^2+y^2=1.

Using first principle show that the derivative of COSX = -SINX

Q. Construct the solution of the heat equation using separation of variables method:

u_xx=4u_t , 0<x<40, t>0

u(0, t)=0, u(40, t)=0, t>0

u(x,0)= x, 0 less than or equal x less than or equal 20, u(x,0)=40-x, 20 less than or equal x less than or equal 40

Q. What is unique solution of a differential equation or a physical problem? Discuss different cases.

Q. What is the resemblance between linear BVPs and systems of algebraic equations Ax=b?

Discuss in terms of solution structure and in particular eigen value problem AX=lambda X

What is the resemblance between linear BVPs and systems of algebraic equations Ax=b?

The side of square are initially 4 inches in length and increase at a constant rate of 3 inches per secondOne corner of suqare moves along a line L at a speed of 2 inches per second for 5 second.During this time the square makes one revolution about p revolving at a constant rate and remaining always perpendicular to L. explain how carefully how to compute volume of solid generated by square.Carry out the computation you describe

1. Create a one-to-one function. It is very important that your function is one-to-one because you will find its inverse. Can't use the function y = x as your one-to-one function.
2. Post a picture of your function's graph.
3. State the window used to graph your function. Carefully choose your window so that it shows as much of the function as possible. Show window on your graphing calculator.
4. Find the inverse of your function.

Determine the volume of the torgus generated by

the revolving circular region enclosed by

(x − 3)²+ y² = 1 about the y-axis.