Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13.3, Problem 31PS
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9. ∇⋅F of F = (2x3y)i-(3y2z)j+(xz3)k at (1,2,-1).
a.
27
b.
-34
c.
4
d.
-7
4. If A andB are differentiable functions of a scalar u, prove that
du (A B) = A. dB
du
d
(a)
dA
du
B
d.
(Ъ)
(A × B) = A × dB
du
dA
du
1. Find the line integral in a vector field
F. dr, where F = (y, x + 2y) and C is
a curve consisting of 2 parts. First, the straight line from (-1,1) to (1,1), followed by
the parabola y = x² from (1,1) to (2,4). You must show all your work.
Chapter 13 Solutions
Calculus
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- 7. Sketch the vector field F = (x − y)î + yĵ. Identify where F₁ vanishes. Identify where F2 vanishes. Plot a few flow lines. 8. Repeat the previous problem for F = yî + (x − y)î.arrow_forwardPlease help with the solution to the following two questions. This is Vector Analysis (Vector Calculus). They have to deal with conservative fields.arrow_forward(a) P, Q and R are differentiable vector functions in R³ and is a scalar u. Show that dQ d[Px (QxR)] = Px[QxdR] + Px[du du du dParrow_forward14arrow_forwardDetermine if each of the following vector fields is the gradient of a function f(x, y). If so, find all of the functions with this gradient. (a) (3x² + e¹0) i + (10x e¹0 - 9 siny) j (b) (10x el0y 9 sin y) i + (3x² + e¹0y) j a) I have placed my work and my answer on my answer sheetarrow_forward6. Compute fF dr where f(x, y) = (y² cos x, 2y sinx) and C is the straight line path starting at (1,1) and ending at (1,3). Hint: is the vector field conservative? (Answer: 8 sin 1)arrow_forwardMatch each vector field with its graph. ? 1. F(x, y) = x² + y} ? + 2. H(2,3) = rỉ s ? 3. G(x, y) = y² + x3 A 1111 B (Click on a graph to enlarge it) сarrow_forward2. Let r = √x² + y² + z². (a) For n ≥ 1 and r > 0, express V(r-n) in terms of r and the radial vector field er. (b) For r> 0, express Vlnr in terms of r and the radial vector field er. (c) Taking A as in question 1, show that for r> 0 we have A(-¹) = 0.arrow_forwardPlease help me.arrow_forward3. An object, initially at A(1, 4, 3), moves in a way that its velocity ar any time t 2 0 is F10) = (a* – 2, 4 , 2t + t2 (a) Find the coordinates of the position of the object at t = 1. (b) Determine the velocity, speed and acceleration at t = 1. (c) Find the scalar tangential and normal components of the acceleration at t = 1. (d) Determine the curvature of the path of the motion at t = 1.arrow_forward4. Consider the motion of a particle as described by 1 1 r(t) = = t, Write the acceleration vector of this particle at time t = 1 as a = a+T+ anÑ. You do not need to find T and Ñ, but you can if you find it helpful.arrow_forwardSuppose we have a vector field Ē(x, y, z) defined by E = -Vộ. Prove or disprove the following assertion: V(V · Ē) = v²Ẽ (4) It might help to write out the components of E in terms of derivatives of ø.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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