1. Use an appropriate linearization to approximate V1.56. • Be sure to include justification. Be clear what function you are lincarizing, what lincarization you are using, and how you obtained the lincarization. Be sure to explain how you use the lincarization you found. • Make sure to include a labeled diagram that shows the function and the tangent line used for your approximation. Is your approximation an under- or over-estimate? How do you know?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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1. Use an appropriate lincarization to approximate V1.56.
• Be sure to include justification. Be clear what function you are lincarizing, what
lincarization you are using, and how you obtained the lincarization. Be sure to
explain how you use the lincarization you found.
• Make sure to include a labeled diagram that shows the function and the tangent
line used for your approximation.
• Is your approximation an under- or over-estimate? How do you know?
Transcribed Image Text:1. Use an appropriate lincarization to approximate V1.56. • Be sure to include justification. Be clear what function you are lincarizing, what lincarization you are using, and how you obtained the lincarization. Be sure to explain how you use the lincarization you found. • Make sure to include a labeled diagram that shows the function and the tangent line used for your approximation. • Is your approximation an under- or over-estimate? How do you know?
Expert Solution
Step 1

Let a function f(x)=x3

Thus, the slope of tangent at the any point on the function, m=f'(x)=13(x)23.

So, the equation of the tangent at any point (x0, f(x0)) of the function is given by

y-f(x0)=m(x-x0)

y=13(x)23(x-x0)+f(x0).

Now, if the tangent is obtained at point (1.56, f(1.56)), or, (1.56, 1.563), then, the equation of tangent is

y=m(x-1.56)+1.563.

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