Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Question
Chapter 10, Problem 7SP
To determine
To find: the first and second derivative of the given function.
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The equation r(t) = (3t + 1) i+ (t - 1) j+ (4t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. Then write the particle's velocity at t=0 as a product of its speed and direction.
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Chapter 10 Solutions
Calculus
Ch. 10.1 - Prob. 1PSCh. 10.1 - Prob. 2PSCh. 10.1 - Prob. 3PSCh. 10.1 - Prob. 4PSCh. 10.1 - Prob. 5PSCh. 10.1 - Prob. 6PSCh. 10.1 - Prob. 7PSCh. 10.1 - Prob. 8PSCh. 10.1 - Prob. 9PSCh. 10.1 - Prob. 10PS
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Prob. 15PSCh. 10.5 - Prob. 16PSCh. 10.5 - Prob. 17PSCh. 10.5 - Prob. 18PSCh. 10.5 - Prob. 19PSCh. 10.5 - Prob. 20PSCh. 10.5 - Prob. 21PSCh. 10.5 - Prob. 22PSCh. 10.5 - Prob. 23PSCh. 10.5 - Prob. 24PSCh. 10.5 - Prob. 25PSCh. 10.5 - Prob. 26PSCh. 10.5 - Prob. 27PSCh. 10.5 - Prob. 28PSCh. 10.5 - Prob. 29PSCh. 10.5 - Prob. 30PSCh. 10.5 - Prob. 31PSCh. 10.5 - Prob. 32PSCh. 10.5 - Prob. 33PSCh. 10.5 - Prob. 34PSCh. 10.5 - Prob. 35PSCh. 10.5 - Prob. 36PSCh. 10.5 - Prob. 37PSCh. 10.5 - Prob. 38PSCh. 10.5 - Prob. 39PSCh. 10.5 - Prob. 40PSCh. 10.5 - Prob. 41PSCh. 10.5 - Prob. 42PSCh. 10.5 - Prob. 43PSCh. 10.5 - Prob. 44PSCh. 10.5 - Prob. 45PSCh. 10.5 - Prob. 46PSCh. 10.5 - Prob. 47PSCh. 10.5 - Prob. 48PSCh. 10.5 - Prob. 49PSCh. 10.5 - Prob. 50PSCh. 10.5 - Prob. 51PSCh. 10.5 - Prob. 52PSCh. 10.5 - Prob. 53PSCh. 10.5 - Prob. 54PSCh. 10.5 - Prob. 55PSCh. 10.5 - Prob. 56PSCh. 10.5 - Prob. 57PSCh. 10.5 - Prob. 58PSCh. 10.5 - Prob. 59PSCh. 10.5 - Prob. 60PSCh. 10 - Prob. 1PECh. 10 - Prob. 2PECh. 10 - 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- - 22 - 2 -2 (3,-4) that has a positive a component. For the function f(x, y) = find a unit tangent vector to the level curve at the pointarrow_forwardProblem 2. Suppose f(x, y) = 10e – 7xe", P =(-2,1), and u is the unit vector in the direction of (5, 2). A. Find the gradient of f(x, y) and evaluate at the point P = (-2,1). Vf = (-7(x*e^x+e^x),20*y*e^(y^2)) (Vf) (P) (-7*(2*e^2+e^2),20*e) B. Find the tangent plane to f(x, y) at the point (-2, 1). z = -7*(2*e^2+e^2)*(x+2)+20*e*(y-1)+10*e+14e^(-2) C. Find the differential df and evaluate at the point (-2, 1) df = -7(x*e^x+e^x)*dx+20*y*e^(y^2)*dy %3D df(-2, 1) = -7*(2*e^2+e^2)*dx+20*e*dy Use the differential at the point (-2, 1) to estimate the change in the values of f(x, y) if x changes by -0.5 and y changes by 0.2. df -7*(2*e^2+e^2)*0.5+20*e*0.2 D. Find the directional derivative of f(x,y) at P = (-2, 1) in the direction of u. D,f = -7*(2*e^2+e^2)*5/sqrt(29)+20*e*2/sqrt(29) E. At the point P = (-2,1), find the direction of maximum ascent. Your answer should be a unit vector. u <-7*(2*e^2+e^2)/sqrt(49*(2*e^2+e^2)^2,400*e^2).: Find the maximum rate of change of f(x, y) at P = (-2, 1).…arrow_forward[1 4] 2. Let D = 2 5 3 6 [4 3] E = 5 6 6 9 a = {B b = {n Suppose now a vector z = {9 + 0 satisfies D'z = 0. Answer the following questions. (1) Find the relations between p, q and r. (2) When some solution vector x = exists to the equation Dx = a, show the necessary condition that a, B and y should satisfy. (3) When some solution vector y = exists to the equation Ey = b, show the necessary condition that 5, 7 and x should satisfy.arrow_forward
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