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c. r(t) = /16 - 4912 i+ 7tj. - sts

c. r(t) = /16 - 4912 i+ 7tj. - sts

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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solve part c

a. Show that n(t) = - g'(t)i + f'(t)j and - n(t) = g'(t)i - f' (t)j are both normal to the curve r(t) = f(t)i + g(t)j at the point (f(t).g(t). To obtain N for a particular plane curve, choose the one of n or -n that points toward the concave side of the curve, and make it into a unit vector. (See the figure to the right.) Apply this method to find N for the following N- T P. curves. b. r(t) = 4ti + 4 e2"j Pot c. (t) = /16 - 49t²i+ 7tj, - sts The vector dT/ds, normal to the curve, always points in the direction in which T is turning. The unit normal vector N is the direction of dT/ds O C. Show that v•T= 0. YD. Show that n•v= 0. Why is the equation from the previous step satisfied? YA. The components of n(t) are the components of v(t) with the order swapped and the sign of one changed, so the dot product is 0. O B. The components of n(t) are negative reciprocals of the components of T, so the dot product is - 1. O C. The components of n(t) are negative reciprocals of the components of v(t), so the dot product is - 1. O D. The sum of the components of v(t) is the negative of T, so the dot product is 0. -2e2t b. N= i+ 4 4 +1 4t 4 e " + 1 c. N = (Di+ ( Di
Transcribed Image Text:a. Show that n(t) = - g'(t)i + f'(t)j and - n(t) = g'(t)i - f' (t)j are both normal to the curve r(t) = f(t)i + g(t)j at the point (f(t).g(t). To obtain N for a particular plane curve, choose the one of n or -n that points toward the concave side of the curve, and make it into a unit vector. (See the figure to the right.) Apply this method to find N for the following N- T P. curves. b. r(t) = 4ti + 4 e2"j Pot c. (t) = /16 - 49t²i+ 7tj, - sts The vector dT/ds, normal to the curve, always points in the direction in which T is turning. The unit normal vector N is the direction of dT/ds O C. Show that v•T= 0. YD. Show that n•v= 0. Why is the equation from the previous step satisfied? YA. The components of n(t) are the components of v(t) with the order swapped and the sign of one changed, so the dot product is 0. O B. The components of n(t) are negative reciprocals of the components of T, so the dot product is - 1. O C. The components of n(t) are negative reciprocals of the components of v(t), so the dot product is - 1. O D. The sum of the components of v(t) is the negative of T, so the dot product is 0. -2e2t b. N= i+ 4 4 +1 4t 4 e " + 1 c. N = (Di+ ( Di
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