Small argument approximations Consider the

Chapter 7, Problem 74E

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QUESTION:

Small argument approximations Consider the following common approximations when x is near zero.

a. Estimate f(0.1) and give the maximum error in the approximation.

b. Estimate f(0.2) and give the maximum error in the approximation.

\(f(x)=\ln (1+x) \approx x-x^{2} / 2\)

Questions & Answers

QUESTION:

Small argument approximations Consider the following common approximations when x is near zero.

a. Estimate f(0.1) and give the maximum error in the approximation.

b. Estimate f(0.2) and give the maximum error in the approximation.

\(f(x)=\ln (1+x) \approx x-x^{2} / 2\)

ANSWER:

Solution 74E

Step 1:

Given that

 The following common approximations when x is near zero.

f(x) = ln(l + x)≈ x − x2/2

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