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Consider the following functions f(x) = sin(x) and g(x) = /8 cos(x). (a) Determine the linearization functions, L₁(x) and L₂(x), for f(x) and g(x), respectively at the center x = T. (b) Use L₁(x) and L₂(x) to estimate sin(3) and 8 cos(3), respectively. (c) Are the approximations L₁(x) and L₂(x) overestimating or underestimating? Sustain your claim using the second derivative.

Consider the following functions f(x) = sin(x) and g(x) = /8 cos(x). (a) Determine the linearization functions, L₁(x) and L₂(x), for f(x) and g(x), respectively at the center x = T. (b) Use L₁(x) and L₂(x) to estimate sin(3) and 8 cos(3), respectively. (c) Are the approximations L₁(x) and L₂(x) overestimating or underestimating? Sustain your claim using the second derivative.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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3 (8 cos(x). - Consider the following functions f(x) = sin(x) and g(x) (a) Determine the linearization functions, L₁(x) and L₂(x), for f(x) and g(x), respectively at the center x = T. (b) Use L₁(x) and L₂(x) to estimate sin(3) and 3/8 cos(3), respectively. (c) Are the approximations L₁(x) and L₂(x) overestimating or underestimating? Sustain your claim using the second derivative. (d) Compute and compare |f"(π)| and g"(π)| to determine which approximation is more accurate.
Transcribed Image Text:3 (8 cos(x). - Consider the following functions f(x) = sin(x) and g(x) (a) Determine the linearization functions, L₁(x) and L₂(x), for f(x) and g(x), respectively at the center x = T. (b) Use L₁(x) and L₂(x) to estimate sin(3) and 3/8 cos(3), respectively. (c) Are the approximations L₁(x) and L₂(x) overestimating or underestimating? Sustain your claim using the second derivative. (d) Compute and compare |f"(π)| and g"(π)| to determine which approximation is more accurate.
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