(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The approximation [tex] e^{x}=1+x+(x^{2}/2) [/tex] is used when [tex] X [/tex] is small estimate the error when [tex]\left|x \right|<0.1[/tex]

2. Relevant equations

[tex]\left|R_{n} \right|<\frac{M(x-a)^{n+1}}{(n+1)!}[/tex]

3. The attempt at a solution

Since the Taylor expansion goes to the second power I used the third derivative of [tex]e^{x}[/tex] which is just its self and found the maximum value that it can be between the domain [0,0.1] which is at [tex]e^{0.1}[/tex] then continuing the formula [tex](0.1-0)^{3}[/tex] then i divided it by 3! which gave me an answer of [tex]1.84*10^{-4}[/tex].

My book on the other hand used [tex]3^{0.1}[/tex] instead of [tex]e^{0.1}[/tex] and as a result the answer in the book was larger than my answer. So which answer is the right answer?

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# Homework Help: Am I right or is my book right (Taylor remainder)

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