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, Problem 45SP
To determine
To find:Thegiven surface integral.
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Chapter 13 Solutions
Calculus
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- Find a unit vector n that is normal to the surface 4z² - x4 - 2y4 = 46 at P = (2, 1, 4) that points in the direction of the xy-plane (in other words, if you travel in the direction of n, you will eventually cross the xy-plane). (Use symbolic notation and fractions where needed.) n =arrow_forwardIncorrect. 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.arrow_forwardSuppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) 4x2 - 2xy xyz (a) Find the rate of change of the potential at P(2, 4, 4) in the direction of the vector v = i + j - k. (b) In which direction does V change most rapidly at P? (c) What is the maximum rate of change at P?arrow_forward
- < . Question 2 of 12 Calculate the line integral of the vector field F = (y, x, x + y) around the boundary curve, the curl of the vector field, and the surface integral of the curl of the vector field. The surface S is the upper hemisphere x² + y + z? = 81, z 2 0 oriented with an upward-pointing normal. (Use symbolic notation and fractions where needed.) F- dr = curl(F) = curl(F) - dS = endentals Publisher WH Freeman Question Source: Rogawskiarrow_forwardIncorrect. 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| ||arrow_forwardA net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by (x - y, z + y + 7, z?) and the net is decribed by the equation y = V1 – x? – z?, y 2 0, and oriented in the positive y- V = direction. (Use symbolic notation and fractions where needed.) v • dS =arrow_forward
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