Use a suitable Maclaurin Series to estimate to five decimal-place accuracy.
A) 0.09528
B) 0.09428
C) 0.09488
D) 0.09478
E) 0.09468

Question

Use a suitable Maclaurin Series to estimate  to five decimal-place accuracy.
A) 0.09528 
B) 0.09428 
C) 0.09488 
D) 0.09478 
E) 0.09468

Quizplus · Accepted Answer

We can use the Maclaurin Series for $e^x$ which is $e^x = \sum_{n=0}^\infty \frac{x^n}{n!}$.
Plugging in $x=\frac{3}{40}$, we get 
$$e^{\frac{3}{40}} \approx \sum_{n=0}^8 \frac{\left(\frac{3}{40}\right)^n}{n!} \approx 0.09478$$
Therefore, the best choice is D, which is closest to our estimate.

Use a Suitable Maclaurin Series to Estimate to Five