1. ## 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.

2. 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.
Apply the formula: Maclaurin Series -- from Wolfram MathWorld

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

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

$f(x)=f(a)+(x-a)\frac{\partial}{\partial x} f(a) + \frac{(x-a)^{2}}{2!} \frac{\partial^{2}}{\partial x^{2}} f(a) + ...$

$f(x) = e^{x}$

and

$a = 0$.

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

$f(a) = e^{0} = 1$
$(x-a)\frac{\partial}{\partial x} f(a)= (x-0)\frac{d}{dx}(e^{0}) = x$

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