Find a series for e^x

• Mar 15th 2011, 04:08 PM
mymony1027
Find a series for e^x
Find a series for e^x.

1) Use to get e^3.
a) How accurate after 10 terms? What is sum of 10 terms?
2) How many to get 0.0001?

Please please please help me with this calculus problem. I am so lost in my class. step by step work would be greatly appreciated. The work does not have to be completely accurate, I just need the steps. Thank you in advance.
• Mar 15th 2011, 04:12 PM
pickslides
$\displaystyle e^x = \sum_{n=0}^{\infty}\frac{x^n}{n!}$
• Mar 15th 2011, 04:24 PM
topsquark
Quote:

Originally Posted by mymony1027
Find a series for e^x.

1) Use to get e^3.
a) How accurate after 10 terms? What is sum of 10 terms?
2) How many to get 0.0001?

Please please please help me with this calculus problem. I am so lost in my class. step by step work would be greatly appreciated. The work does not have to be completely accurate, I just need the steps. Thank you in advance.

Taylor series
$\displaystyle f(x) \approx f(a) + f'(a) \cdot (x - a) + \frac{f''(a)}{2!}(x - a)^2 + \frac{f'''(a)}{3!}(x - a)^3 + ~...~$

So what are the derivatives of $e^x$ ?

-Dan
• Mar 15th 2011, 06:46 PM
Prove It
Quote:

Originally Posted by topsquark
Taylor series
$\displaystyle f(x) \approx f(a) + f'(a) \cdot (x - a) + \frac{f''(a)}{2!}(x - a)^2 + \frac{f'''(a)}{3!}(x - a)^3 + ~...~$

So what are the derivatives of $e^x$ ?

-Dan

And of course, it's easiest if you choose to centre your series about $\displaystyle a = 0$, since $\displaystyle e^a$ can be evaluated exactly...