Maclaurin Series -- from Wolfram MathWorld
Please show what work you've done. Where are you stuck?
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.