taylor expansion

Calculate the first 5 terms of the taylor expansion of e^x about x=0.


Use the first four terms of the above expansion to approximate e^0.5. Answer to 6 d.p.


Finally, use the final term to estimate the error in your approximation. Answer to 3 sig figures.

Quote:

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Originally Posted by mr_motivator

Calculate the first 5 terms of the taylor expansion of e^x about x=0.


Use the first four terms of the above expansion to approximate e^0.5. Answer to 6 d.p.


Finally, use the final term to estimate the error in your approximation. Answer to 3 sig figures.

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Apply the formula: Maclaurin Series -- from Wolfram MathWorld

Please show what work you've done. Where are you stuck?

Alright, well the Taylor series expansion for a function f(x) about the point x = a is given by:



So in your case,



and

.

so using the above formula, the first two terms are:




And you can find the remaining three in that same way...