Answer:
To approximate ln(1.2) using the first three terms in the series expansion of ln(1+x), we can use the formula:
ln(1+x) = x - (x^2)/2 + (x^3)/3
Substituting x = 0.2 into the formula, we get:
ln(1.2) ≈ 0.2 - (0.2^2)/2 + (0.2^3)/3
Calculating this approximation gives:
ln(1.2) ≈ 0.2 - 0.02 + 0.008/3 ≈ 0.2 - 0.01 + 0.0027 ≈ 0.189
Now, let's calculate the percentage error in this approximation compared to the actual value of ln(1.2).
Percentage error = (Approximated value - Actual value) / Actual value * 100
Percentage error = (0.189 - ln(1.2)) / ln(1.2) * 100
Using a calculator, we can find the actual value of ln(1.2) as approximately 0.1823.
Percentage error = (0.189 - 0.1823) / 0.1823 * 100 ≈ 3.68%
Therefore, the percentage error in the value obtained is approximately 3.68% (2 s.f.).
Explanation: