7. Normals to plane curves 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(1)). %3D To obtain N for a particular plane curve, we can choose the one of n or -n from part (a) that points toward the concave side of the curve, and make it into a unit vector. (See Figure 13.19.) Apply this method to find N for the following curves. b. r(t) = ti + e2'j c. r(t) = V4 – fi + tj, -2< t< 2

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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7. Normals to plane curves
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(1)).
%3D
To obtain N for a particular plane curve, we can choose the one of
n or -n from part (a) that points toward the concave side of the
curve, and make it into a unit vector. (See Figure 13.19.) Apply
this method to find N for the following curves.
b. r(t) = ti + e2'j
c. r(t) = V4 – fi + tj, -2< t< 2
Transcribed Image Text:7. Normals to plane curves 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(1)). %3D To obtain N for a particular plane curve, we can choose the one of n or -n from part (a) that points toward the concave side of the curve, and make it into a unit vector. (See Figure 13.19.) Apply this method to find N for the following curves. b. r(t) = ti + e2'j c. r(t) = V4 – fi + tj, -2< t< 2
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