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) = √t² + √√t³ĵ + tk on the interval [1,4]. Evaluate it numerically. 7. Find the directional derivative of the function w = arcsin xyz at the point (1,½½, 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) = √t² + √√t³ĵ + tk on the interval [1,4]. Evaluate it numerically. 7. Find the directional derivative of the function w = arcsin xyz at the point (1,½½, in the direction of = (-1,3,-2). In what direction is the directional derivative a maximum?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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) = √t² + √√t³ĵ + tk on the interval [1,4].
Evaluate it numerically.
7. Find the directional derivative of the function w = arcsin xyz at the point (1,½½, 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%2F16cca446-9c78-4e8e-bc07-01fccefbcd20%2Fmullpta_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) = √t² + √√t³ĵ + tk on the interval [1,4].
Evaluate it numerically.
7. Find the directional derivative of the function w = arcsin xyz at the point (1,½½, in the direction
of = (-1,3,-2). In what direction is the directional derivative a maximum?
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