Let f (x, y) = e^x (sin(y) +1) and use the point P (0, (pi/2)) a. Find the gradient of f at P. b. Find the directional tangent line for the unit vector u in the direction of v = <1,2 >, at P; note that f(0, (pi/2)) =2 c. Find the normal line at P. d. Find the tangent plane to f at p

Let f (x, y) = e^x (sin(y) +1) and use the point P (0, (pi/2)) a. Find the gradient of f at P. b. Find the directional tangent line for the unit vector u in the direction of v = <1,2 >, at P; note that f(0, (pi/2)) =2 c. Find the normal line at P. d. Find the tangent plane to f at p

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter5: Graphs And The Derivative

Section5.1: Increasing And Decreasing Functions

Problem 44E: Where is the function defined by f(x)=ex increasing? Decreasing? Where is the tangent line...

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Question

Let f (x, y) = e^x (sin(y) +1) and use the point P (0, (pi/2))

a. Find the gradient of f at P.
b. Find the directional tangent line for the unit vector u in the direction of v = <1,2 >, at P; note that f(0, (pi/2)) =2
c. Find the normal line at P.
d. Find the tangent plane to f at p

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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