Question: (Section 3.1) Approximate both ln(0.99) and ln(1.01) using one tangent line approximation:First note that ln(0.99) and ln(1.01) both ~~ln(1).Let f(x)=ln(x). Then, f^(')(x)=Let x_(0)=1. Then f^(')(1)=L(x),
(Section 3.1) Approximate both ln(0.99) and ln(1.01) using one tangent line approximation:First note that ln(0.99) and ln(1.01) both ~~ln(1).Let f(x)=ln(x). Then, f^(')(x)=Let x_(0)=1. Then f^(')(1)=L(x), the line tangent to l(n)/(bar)((x)) at x_(0)=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:ln(0.99)~~ln(1.01)~~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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