Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)
6th Edition
ISBN: 9781524908102
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13, Problem 44SP
To determine
To find:The given surface
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Please help. This problem involves finding the amount of work done over a path using a line integral. Thank you.
20. Let S be an oriented surface parametrized by r(u,v). Define the
notation do = r, du × r, dv so that do is a vector normal to
the surface. Also, the magnitude do =
face area (by Equation 5 in Section 16.5). Derive the identity
do is the element of sur-
do = (EG – F²)'/² du dv
where
E = r?, F = r„ • r,,
and G = |r,|?.
Kindly solve the task step by step
Chapter 13 Solutions
Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)
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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.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 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_forward2. Find the curl of the vector field. F = z°e* sin(2 y)i – e' cos yj+ xyzk toarrow_forward
- - y², Consider the vector field F = (2x, 3y, 4z) and the surface z = 4-2² Write down the line integral and the surface integral that Stokes' Theorem tells us are equal vector field and surface. Evaluate both. Hint: The surface integral requires very little work. You do not even need to parameterize the surface. 2 ≥ 0. for thisarrow_forwardx (u, v) = (u² - cos v, u + sın t, cosarrow_forwardChoose the correct answer/s. Choose E if none of the choices is correct.arrow_forward
- 4. Given r(t) =ti+t²j. Find the unit tangent vector and principal unit normal vector when t=1.arrow_forward3.4 You are given a vector function A and an open surface S bounded by C. Determine the curl of each vector function and verify both sides of Stokes's theorem on S and along C. TT S:r= 5, 6. TT TT A = 2 a, + 5r sin 0 cos o a, + 4 cos 0 as 4arrow_forward5. Let C be the portion of the parabola y = x², oriented from the starting point (0, 0) towards the end point (3,9). Find the unit tangent vector T and the unit normal vector n to C at the point (1, 1).arrow_forward
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