# Thread: Value of Taylor Series

1. ## Value of Taylor Series

I am stuck on finding out the value of two terms of the Taylor series for this equation:

$\displaystyle x^5e^{x^3}$

and also that this Taylor Series is centered near $\displaystyle x = 0$ and at this point, the first few terms of this series looks like:

$\displaystyle x^5+x^8+\frac {x^{11}} {2!}+\frac {x^{14}} {3!}+ \frac {x^{17}} {4!}+....$

Finally, I am supposed to determine the values at the 1st and 11th term, again near $\displaystyle x = 0$.

Wouldn't both terms be 0 though since the value is dependent upon the x value, which is 0, or am I missing something? Thanks for the help.

2. Originally Posted by Spudwad
I am stuck on finding out the value of two terms of the Taylor series for this equation:

$\displaystyle x^5e^{x^3}$

and also that this Taylor Series is centered near $\displaystyle x = 0$ and at this point, the first few terms of this series looks like:

$\displaystyle x^5+x^8+\frac {x^{11}} {2!}+\frac {x^{14}} {3!}+ \frac {x^{17}} {4!}+....$

Finally, I am supposed to determine the values at the 1st and 11th term, again near $\displaystyle x = 0$.

Wouldn't both terms be 0 though since the value is dependent upon the x value, which is 0, or am I missing something? Thanks for the help.
You are probably missing something, please post the exact wording of the problem.

CB

3. Hi Spudwad,

The function value (for x=0) is only not zero for the (3n+5)th derivative. With n is a real positive integer. This meas that only the (3n+6)th terms in de serie are not equal to zero.

Since 1 and 11 are both not a (3n+6) term, they have to be zero.

Good luck!