Question Solved1 Answer 1. A particle moves in the xy-plane so that the position of the particle at any time t is given by x(t) = 2 e^(3) + e^(-7t), y(t) = 3 e^(3t) - ел(-2t). a. Find the velocity vector for the particle in terms of t and find the speed of the particle at t=0. b. Find dy/dx in terms of t and find lim as t approaches infinity of dy/dx. C. Find each value of t at which the line tangent to the path of the particle is horizontal, or explain why none exists. d. Find each value of t at which the line tangent to the path of the particle is vertical or explain why none exists.

HSEVTH The Asker · Calculus

Transcribed Image Text: 1. A particle moves in the xy-plane so that the position of the particle at any time t is given by x(t) = 2 e^(3) + e^(-7t), y(t) = 3 e^(3t) - ел(-2t). a. Find the velocity vector for the particle in terms of t and find the speed of the particle at t=0. b. Find dy/dx in terms of t and find lim as t approaches infinity of dy/dx. C. Find each value of t at which the line tangent to the path of the particle is horizontal, or explain why none exists. d. Find each value of t at which the line tangent to the path of the particle is vertical or explain why none exists.
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Transcribed Image Text: 1. A particle moves in the xy-plane so that the position of the particle at any time t is given by x(t) = 2 e^(3) + e^(-7t), y(t) = 3 e^(3t) - ел(-2t). a. Find the velocity vector for the particle in terms of t and find the speed of the particle at t=0. b. Find dy/dx in terms of t and find lim as t approaches infinity of dy/dx. C. Find each value of t at which the line tangent to the path of the particle is horizontal, or explain why none exists. d. Find each value of t at which the line tangent to the path of the particle is vertical or explain why none exists.
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(a){:[x(t)=2e^(3t)+e^(-7t)quad y(t)=3e^(3t)-e^(-2t)],[(dx)/(dt)=6e^(3t)-7e^(-7t)quad(dy)/(dt)=9e^(3t)+2e^(-2t)],[V(t)=(:x^(')(t,y^(')(t):):}],[V(t)=(:6e^(3t)-7e^(-7t),9e^(3t)+2e^(-2t):)],[V(0)=(:6-7","9+2:)],[V(0)=(:-1","11:)],[(dy)/(dx)=(dy)/(dt)//(dx)/(dt)=((9e^(3t)+2e^(-2t))/(6e^(3t)-7e^(-7t)):}],[" (b) ... See the full answer