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4. This problem considers y = In r. (a) Find approximations to In(1.1) and In(0.9) using a first degree Taylor Polynomial. (b) Use a calculator to decide if these approximations are too high or too low. (c) Sketch the graph of y = lIn r and the tangent line at r = 1. Can you explain your answer to the previous part based on your picture?

4. This problem considers y = In r. (a) Find approximations to In(1.1) and In(0.9) using a first degree Taylor Polynomial. (b) Use a calculator to decide if these approximations are too high or too low. (c) Sketch the graph of y = lIn r and the tangent line at r = 1. Can you explain your answer to the previous part based on your picture?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Problem 4: Understanding Natural Logarithms with Taylor Polynomials This problem considers the natural logarithm function \( y = \ln x \). #### (a) Find Approximations Find approximations to \( \ln(1.1) \) and \( \ln(0.9) \) using a first-degree Taylor Polynomial. #### (b) Evaluate Approximations Use a calculator to decide if these approximations are too high or too low. #### (c) Graphing and Analysis Sketch the graph of \( y = \ln x \) and the tangent line at \( x = 1 \). Can you explain your answer to the previous part based on your picture?
Transcribed Image Text:### Problem 4: Understanding Natural Logarithms with Taylor Polynomials This problem considers the natural logarithm function \( y = \ln x \). #### (a) Find Approximations Find approximations to \( \ln(1.1) \) and \( \ln(0.9) \) using a first-degree Taylor Polynomial. #### (b) Evaluate Approximations Use a calculator to decide if these approximations are too high or too low. #### (c) Graphing and Analysis Sketch the graph of \( y = \ln x \) and the tangent line at \( x = 1 \). Can you explain your answer to the previous part based on your picture?
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