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## Main Question or Discussion Point

Hello all,

My question is in regards to the Taylor series expansion of

[tex]f(x)=e^x=1+x+x^2/(2!)+x^3/(3!).......[/tex]

I calculated the value of

[tex]e^(-2)[/tex]

using the first 4 terms, 6 terms, and then the first 8 terms. I then calculated the relative error to compare it to the true value, depcited by my calculator to 6 significant figures. Using the first four terms, I found an error of 2609%. Using the first 6 terms I found an error of 2905%, and lastly using the first 8 terms I found an error of 2952%.

What can I conclude from this? Does the error increase (at a decreasing rate) until it begins decreasing (at an increasing rate)?

My question is in regards to the Taylor series expansion of

[tex]f(x)=e^x=1+x+x^2/(2!)+x^3/(3!).......[/tex]

I calculated the value of

[tex]e^(-2)[/tex]

using the first 4 terms, 6 terms, and then the first 8 terms. I then calculated the relative error to compare it to the true value, depcited by my calculator to 6 significant figures. Using the first four terms, I found an error of 2609%. Using the first 6 terms I found an error of 2905%, and lastly using the first 8 terms I found an error of 2952%.

What can I conclude from this? Does the error increase (at a decreasing rate) until it begins decreasing (at an increasing rate)?