AS/A2 Pure 4 Pure 5

P6 Topic 4: Maclaurin and Taylor series
The power series for ex
The display shows the graph of y = ex. Also shown is the graph of the curve:
By using the slider you can vary the value of n from 0 to 20 (only the integer values are valid) and see how closely the power series matches the curve y = ex.

This display shows the same information numerically. Keep x as 1, and hence find what value of n gives e correct to 8 decimal places.

Summary Clearly, as n becomes bigger, the curve of the equation: becomes closer to the curve of y = ex. Convergence is quite slow. You will need to make n=7 and x=1 to get an approximation to e that is correct to 3 decimal places. For 8 decimal place accuracy you will need to make n=11 and x=1. Based on free Java applets from JavaMath