(1 point) Approximate both In(0.98) and In(1.02) using First note that In(0.98) and In(1.02) both In(1). Let f(x) = ln(x). Then, f'(x) = 1/x Let xp = 1. Then f'(1) = | L(x), the line tangent to In(x) at xo = 1 is: L(x)= Note that the tangent line is a good approximation to t values below: In(0.98) In(1.02) ≈ Hint: If you put the exact values into your calculator yo
(1 point) Approximate both In(0.98) and In(1.02) using First note that In(0.98) and In(1.02) both In(1). Let f(x) = ln(x). Then, f'(x) = 1/x Let xp = 1. Then f'(1) = | L(x), the line tangent to In(x) at xo = 1 is: L(x)= Note that the tangent line is a good approximation to t values below: In(0.98) In(1.02) ≈ Hint: If you put the exact values into your calculator yo
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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Transcribed Image Text:(1 point) Approximate both In(0.98) and In(1.02) using one tangent line approximation:
First note that In(0.98) and In(1.02) both In(1).
Let f(x) = ln(x). Then, f'(x) = 1/x
Let xo = 1. Then f'(1) = ||
L(x), the line tangent to In(x) at xo = 1 is:
L(x) =
Note that the tangent line is a good approximation to the function f(x) close to the point of tangency. Use the tangent line approximation to estimate the
values below:
In(0.98)
In(1.02)
Hint: If you put the exact values into your calculator you won't get the right answer, but your answer should be close to the exact values.
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