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The value of the integral ∬ S F → ⋅ N → d S for the vector field F → = 2 x i ^ − 3 y j ^ and S is the part of the hemisphere x 2 + y 2 + z 2 = 5 for z ≥ 1 .

The value of the integral ∬ S F → ⋅ N → d S for the vector field F → = 2 x i ^ − 3 y j ^ and S is the part of the hemisphere x 2 + y 2 + z 2 = 5 for z ≥ 1 .

Solution Summary: The author calculates the value of the integral displaystyle 'underset'Siint'sstackreltoFcdot

Calculus

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 13.5, Problem 38PS

To determine

To calculate: The value of the integral ∬SF→⋅N→dS for the vector field F→=2xi^−3yj^ and S is the part of the hemisphere x2+y2+z2=5 for z≥1 .

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Chapter 13.5, Problem 37PS

Chapter 13.5, Problem 39PS

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1. For each curve, construct dr. • Let Ci be r? + y² = 16 • Let C2 be y = 5 – 2x • Let C3 be r = 2 – y? 2. Create a plot of each vector field below. F = y& +5 ŷ • G = -4x x – 4y ŷ • H= =&+rŷ 3. Compute fe, F- dĩ 4. Compute fe G · dr 5. Сompute fo Н. dr

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Incorrect. Use a computer or calculator with Euler's method to approximate the flow line through (1, 2) for the vector field v = y² i + 1.1x² j using 5 steps with At = 0.1. Find the exact values of x1,.…. ,X5 and yı, , y5 and then fill in the blanks rounding your numbers to •.... three decimal places. X1 = i 1.1 ,Yi = i 2.51 X2 i 1.2 ,y2 3.273 X3 = i 1.3 ,Y3 = i 4.50283 X4 = i 1.4 , Y4 i 6.7162 X5 = i 1.5 , Y5 = i 11.4427 eTextbook and Media Hint I| ||

Chapter 13 Solutions

Calculus

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Incorrect. Use a computer or calculator with Euler's method to approximate the flow line through (1, 2) for the vector field v = y² i +1.1x² j using 5 steps with At = 0.1. Find the exact values of x1, ... , x5 and y1, ... , y5 and then fill in the blanks rounding your numbers to three decimal places. X1 = !Yı = i X2 i 1.2 , y2 3.273 X3 = i 1.3 Y3 = i 4.50283 X4 i 1.4 6.7162 X5 = i 1.5 Y5 = i 11.4427 eTextbook and Media Assistance Used Hint Assistance Used The vector field is given by v = y i + 1.1x² j , that is, the flow line (x (t), y (t)) satisfies x' (t) = y² y' (t) = 1.1x².
Mark the correct statements. i.The value of the vector field can also be just a real number. ii.All vectors in the vector field F（r）= −r/2 point towards the origin. Here r is the position vector of the point (x,y,z). iii.A charged particle always moves along the field line of the electric field if it is not acted upon by other forces. iv.The field lines of a vector field can sometimes be closed curves.
A4. Which of the following vector fields is not the curl of another vector field? A. F=zi+zj+yk B. F= ²1-2ryj+5k C. F=3ri-2yj-zk D. F=zi+yj+zk E. F= 21+2+4k Conti

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