Use the remainder term to estimate the maximum error in the following approximat

Question

Use the remainder term to estimate the maximum error in the following approximation on the given interval. e^x almostequalto l + x + x^2/2; [-3/10,3/10] Select: the correct choice below and fill in the answer box to complete your choice. (Use scientific notation. Round to two decimal places as needed.) The maximum error is approximately squarebox for M=2. The maximum error is approximately squarebox for M=1. The maximum error is approximately squarebox for M = 3/10^- The maximum error is approximately squarebox for M=-1/e^-.

Explanation / Answer

The series extends as
e ^(x) = 1 + x + x^2/2

Note that, because on the given interval we have |x|<1, the remainder after first term will be less than x on the interval (-3/10, 3/10) .
So the maximum error will be 3/10 --------------answer.

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