Sue M.

# gradient fields and exact differentials

A. let f(x,y)= xexy, and C be the path y=1/x from (1,1) to (0,∞)
1. calculate F=∇f
2. Calculate the integral ∫cF*dr
- directly
- by using the fundamental theorem for line integrals

B. Left f(x,y) = sinxcosx
1. calculate F=∇f

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Experienced Math Tutor

Sue M.

thank you for the help!
For part B i got F=<cos2x-sin2x, 0> is that correct?

if so,
1.what is the maximum value ∫cF*dr can have over all possible paths C in the plane?
2.What is the path that C can have for which this maximum value is attained?

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06/24/16

Darryl K.

Yes.  I cannot answer the other 2 questions right away.  I will get with you Saturday night.
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06/24/16

Sue M.

thank you!
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06/25/16

Darryl K.