1. Find the equation of the tangent line to y = r at z = 1. Solution. To get the equation of the line, we need the point P(ro, y0) and the slope m. We are only given ro = 2. However, the y-coordinate of ro is easy to find by substituting ro 2 into y r. This gives us yo =. Hence, P has the coordinates Now, we look for the slope: y =r lim y-Yo = lim 220 I- ro P Finally, the equation of the tangent line with slope and passing through P is

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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Find the missing piece

1. Find the equation of the tangent line to y =r at r = 1.
Solution. To get the equation of the line, we need
the point P(ro, y0) and the slope m. We are only
given ro = 2. However, the y-coordinate of ro is
easy to find by substituting ro = 2 into y = r. This
gives us yo = . Hence, P has the coordinates
Now, we look for the slope:
y = r?
lim -Y0
= lim
P
Finally, the equation of the tangent line with slope
and passing through P
m
is
Transcribed Image Text:1. Find the equation of the tangent line to y =r at r = 1. Solution. To get the equation of the line, we need the point P(ro, y0) and the slope m. We are only given ro = 2. However, the y-coordinate of ro is easy to find by substituting ro = 2 into y = r. This gives us yo = . Hence, P has the coordinates Now, we look for the slope: y = r? lim -Y0 = lim P Finally, the equation of the tangent line with slope and passing through P m is
2. Find the slope-intercept form of the
tangent line to f(z) = VE at z = 4.
%3D
VE
Basic Calculus
Lesson 4 Page 4
Solution. Again, we find the y-coordinate of ro = 4: yo =
Hence, P has
coordinates (4, 2). Now, we look for the slope of the tangent line. Notice that
we have to rationalize the numerator to evaluate the limit..
/(z)-/(ro)
= lim
m= lim
lim
lim
Finally, with point P
land slope m
the equation of the tangent line is
Page 6 10
Transcribed Image Text:2. Find the slope-intercept form of the tangent line to f(z) = VE at z = 4. %3D VE Basic Calculus Lesson 4 Page 4 Solution. Again, we find the y-coordinate of ro = 4: yo = Hence, P has coordinates (4, 2). Now, we look for the slope of the tangent line. Notice that we have to rationalize the numerator to evaluate the limit.. /(z)-/(ro) = lim m= lim lim lim Finally, with point P land slope m the equation of the tangent line is Page 6 10
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