How to find Approximation of "e" to the power of x^3 near x=0

[Bluewolf1986]

I need help solving this problem: Find the a non-linear polynomial approximation of e^x^3 near x=0 using an e^u substitution formula.
I set up the approximation as follows to try to find the answer: u= x^3, e^x^3 = e^u ~ 1+u ~ 1+x^3

Please help, I would appreciate it. Thank you.

 

[Deleted member 4993]

I need help solving this problem: Find the a non-linear polynomial approximation of e^x^3 near x=0 using an e^u substitution formula.
I set up the approximation as follows to try to find the answer: u= x^3, e^x^3 = e^u ~ 1+u ~ 1+x^3

Please help, I would appreciate it. Thank you.

Please post the EXACT assignment (word for word) as it was presented to you. Please include reference to class topics with this assignment.

Are you familiar with Taylor's expansion?

 

[HallsofIvy]

I need help solving this problem: Find the a non-linear polynomial approximation of e^x^3 near x=0 using an e^u substitution formula.
I set up the approximation as follows to try to find the answer: u= x^3, e^x^3 = e^u ~ 1+u ~ 1+x^3

Please help, I would appreciate it. Thank you.

You have already done exactly what you were asked to do. The MacLaurin polynomial, to first degree (so the linear approximation around x= 0) for \(\displaystyle e^u\) is \(\displaystyle 1+ u\) and since \(\displaystyle u= x^3\) a non-linear approximation for \(\displaystyle e^{x^3}\) is \(\displaystyle 1+ x^3\)

 

[Bluewolf1986]

Thanks!