Find a series for e^x

**mymony1027** · March 15th 2011, 03:08 PM

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.

**pickslides** · March 15th 2011, 03:12 PM

$\displaystyle e^x = \sum_{n=0}^{\infty}\frac{x^n}{n!}$

**topsquark** · March 15th 2011, 03:24 PM

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

**Prove It** · March 15th 2011, 05:46 PM

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...

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