Taylor expansion help: trying to solve this limit by expanding an exponential function to the second order in x=0

[Anakin_99]

Hi guys I was trying to solve this limit by expanding an exponential function to the second order in x=0 using the generic Taylor polynomial formula but I don't understand where I'm wrong.
I know the specific taylor expansion for the exponential but where am I wrong using the generic one ? Why is it different ? Also why is the rest wrong ?
I attached 2 files to explain my problem.
Sorry if my English is bad I hope you can help me.

 

[Dr.Peterson]

Hi guys I was trying to solve this limit by expanding an exponential function to the second order in x=0 using the generic Taylor polynomial formula but I don't understand where I'm wrong.
I know the specific taylor expansion for the exponential but where am I wrong using the generic one ? Why is it different ? Also why is the rest wrong ?
I attached 2 files to explain my problem.
Sorry if my English is bad I hope you can help me.

You forgot to evaluate f(0), f'(0), etc. at zero before using them in the formula. Your x's in the fourth line are a mix of the actual x's and 0's.

From the second line, f'(0) = 0, f"(0) = -4.

 

[Anakin_99]

thank you now I understand, have a nice day you really helped me.