Consider the curve parametrized by x www = 1 + ln(t) and y = t¹ + 2t. dy a) First eliminate the parameter t to compute in terms of x and y. dx b) Next, use the fact that dy dx to compute in terms of t. dy da c) Lastly, use either your answer from part a) or part b) to find the slope of the tangent line when t 1 and (x, y) = (1,3). = =

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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Consider the curve parametrized by x
www
1 + ln(t) and y = t4 + 2t.
dy
a) First eliminate the parameter t to compute
in terms of x and y.
dx
b) Next, use the fact that
dy
dx
to compute
dy
dx
in terms of t.
c) Lastly, use either your answer from part a) or part b) to find the slope of the tangent
line when t= =
1 and (x, y) = (1,3).
||
Transcribed Image Text:Consider the curve parametrized by x www 1 + ln(t) and y = t4 + 2t. dy a) First eliminate the parameter t to compute in terms of x and y. dx b) Next, use the fact that dy dx to compute dy dx in terms of t. c) Lastly, use either your answer from part a) or part b) to find the slope of the tangent line when t= = 1 and (x, y) = (1,3). ||
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