Calculus Answers

In this project you will investigate the relationship between the coefficients of a monic polynomial

and its roots or zeros.

In your final formal submission address each of the following questions using the guidelines provided

in the excerpts from “Some Remarks on Writing Mathematical Proofs”. Your submission should

not be an itemized list of worked out solutions to each of the problems, but instead should be a

formal, typeset document including an introduction, motivation, justification, and conclusion.

6.What relationship do you find between the zeros of the polynomial and the coefficients of the

polynomial? Can you state some general formulas? How do you think this pattern would

extend to a degree five monic polynomial? degree six? degree 10? degree n? Will these

formulas always work? Explain. Why do you think having formulas like this would be useful? Explain

3. A through filled with liquid is 2m long and has a cross section of an isosceles trapezoid 30cm width at the bottom, 60cm width on top and 50cm depth. If the through leaks water at the rate of 2000 cm^3/min , how fast is the water level decreasing when the water is 20cm deep.

How do you evaluate ∫c (x^2 +yz) dz where C is given by x=t, y=t^2 , z=3t and 1≤t≤2?

A)143/2

B)163/4

C)153/4

D)133/4

Find the solution of the partial Differential equation (D^2-D^1^2) z=0? A) z=Φ1(x-y) +Φ2(x-y) B) z=Φ1(x+y) +Φ2(x+y) C) z=Φ1(x-y)-Φ2(x-y) D) z=Φ1(x+y) +Φ2(x-y)