Show complete solution. Let w= F(x,y,x) = -x2tan(yz) + ez+1 ln(xy) and let P be the point (1,e,0). a. Find the rate of change of F at P in the direction of the vector (-2,1,2) b. What is the maximum rate of change of f at P? c. If x= s2-t, y= s+2t2 and z=sin(πt), use the chain rule to find ∂w/∂s when (s,t)=(1.0).

Show complete solution. Let w= F(x,y,x) = -x2tan(yz) + ez+1 ln(xy) and let P be the point (1,e,0). a. Find the rate of change of F at P in the direction of the vector (-2,1,2) b. What is the maximum rate of change of f at P? c. If x= s2-t, y= s+2t2 and z=sin(πt), use the chain rule to find ∂w/∂s when (s,t)=(1.0).

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter2: Functions And Graphs

Section2.6: Proportion And Variation

Problem 18E

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Question

Show complete solution.
Let w= F(x,y,x) = -x²tan(yz) + e^z+1 ln(xy) and let P be the point (1,e,0).
a. Find the rate of change of F at P in the direction of the vector (-2,1,2)
b. What is the maximum rate of change of f at P?
c. If x= s²-t, y= s+2t² and z=sin(πt), use the chain rule to find ∂w/∂s when (s,t)=(1.0).

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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