5. Evaluate √ · dr using Stokes' Theorem for F(x, y, z) = zî + xĵ + xyzk for S: z = x² − y², 0 ≤ x ≤ 1,0 ≤ y ≤ 1. 6. Write an integral for the arc length of the curve (t) = √t²î + √t³ĵ + tk on the interval [1,4]. Evaluate it numerically. 7. Find the directional derivative of the function w = arcsin xyz at the point (1,1,1) in the direction of (-1,3,-2). In what direction is the directional derivative a maximum?
5. Evaluate √ · dr using Stokes' Theorem for F(x, y, z) = zî + xĵ + xyzk for S: z = x² − y², 0 ≤ x ≤ 1,0 ≤ y ≤ 1. 6. Write an integral for the arc length of the curve (t) = √t²î + √t³ĵ + tk on the interval [1,4]. Evaluate it numerically. 7. Find the directional derivative of the function w = arcsin xyz at the point (1,1,1) in the direction of (-1,3,-2). In what direction is the directional derivative a maximum?
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.
Chapter6: Applications Of The Derivative
Section6.4: Related Rates
Problem 9E: Assume xand yare functions of t.Evaluate dy/dtfor each of the following. cos(xy)+2x+y2=2; dxdt=2,...
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I need help with this problem and an explanation for the solution described below. (Calculus 3):
![5. Evaluate √ · dr using Stokes' Theorem for F(x, y, z) = zî + xĵ + xyzk for S: z = x² − y²,
0 ≤ x ≤ 1,0 ≤ y ≤ 1.
6. Write an integral for the arc length of the curve (t) = √t²î + √t³ĵ + tk on the interval [1,4].
Evaluate it numerically.
7. Find the directional derivative of the function w = arcsin xyz at the point (1,1,1) in the direction
of (-1,3,-2). In what direction is the directional derivative a maximum?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea56b2d3-976b-48ba-b1de-ef5a4d536379%2F66314e31-3c17-4887-a719-1f4445b17dfa%2F0hctdhn_processed.png&w=3840&q=75)
Transcribed Image Text:5. Evaluate √ · dr using Stokes' Theorem for F(x, y, z) = zî + xĵ + xyzk for S: z = x² − y²,
0 ≤ x ≤ 1,0 ≤ y ≤ 1.
6. Write an integral for the arc length of the curve (t) = √t²î + √t³ĵ + tk on the interval [1,4].
Evaluate it numerically.
7. Find the directional derivative of the function w = arcsin xyz at the point (1,1,1) in the direction
of (-1,3,-2). In what direction is the directional derivative a maximum?
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