Calculus Answers

solve the initial value problem y' + 3y =f(t) ,y(0)=1 where f(t) = 1 for 0<=t<1 and 0, t>=1

1. Consider the graph of the function y = sin x + cos x. Describe its overall shape.

• Is it periodic?
• How do you know?

2. Using a graphing calculator or other graphing device, estimate the x- and y-values of the maximum point for the graph (the first such point where x > 0). It may be helpful to express the x-value as a multiple of π.

3. Now consider other graphs of the form y = A sin x + B cos x for various values of A and B.

• Sketch the graph when A = 2 and B = 1, and, find the x - and y-values for the maximum point. (Remember to express the x-value as a multiple of π, if possible.)
• Has it moved?

4. Repeat and sketch the graph for A = 1, B = 2.

• Is there any relationship to what you found in part (2)?

5. Explain what you have discovered from completing this activity using details and examples.

Find the average value of f (x, y) over the region R f(x, y) = ex + y R: triangle with vertices (0, 0), (0, 3), (3, 3) with maple lab

1. To reduce shipping distances between the manufacturing facilities and a major consumer, acomputer brand, intends to start production of a new controlling chip for Pentium III mi-croprocessors at their two Asian plants.  The cost of producingx1chips at India isC1=0.002x21+ 4x1+ 500,and the cost of producingx2chips at Singapore isC2= 0.005x22+ 4x2+ 275.The Indian computer manufacturer buys them for $150 per chip. Find the quantity that shouldbe produced at each Asian location to maximize the profit if, in accordance with Intel’s mar-keting department, it is described by the expression:P(x1, x2) = 150(x1+x2)−C1−C2.2.