How many nonzero terms of the known Maclaurin series for ln(1 + x) are needed to approximate ln(1.1) correct to 4 decimal places?
A) 2
B) 3
C) 6
D) 9
E) 4

Question

Quizplus · Accepted Answer

The Maclaurin series for ln(1 + x) is x - x^2/2 + x^3/3 - x^4/4 + ... . To approximate ln(1.1) to 4 decimal places, we substitute x = 0.1 and look for the point at which additional terms contribute less than 0.00005 (half of 10^-4, due to rounding) to the sum. The third term, 0.1^3/3, is less than 0.00005, making the first two terms sufficient for the approximation. However, to ensure the approximation is correct to 4 decimal places, we include the third term, which affects the fourth decimal place due to rounding.

How Many Nonzero Terms of the Known Maclaurin Series for Ln(1