well, we could simplify to get and use the fact exponentials grow faster than polynomials to conclude the limit goes to zero.
if you do not like that, there is always the option of expressing as a power series from the begining, or in the new expression we got from L'Hopital's. the same conclusion follows
yes, that is fine. once we can express the function as a power series around zero and it is differentiable at zero, we know it is infinitely differentiable, and we can find it's derivative by differentiating the power series term by term. do you have to actually come up with a formula for the nth derivative? if so, it is still beneficial to start with the power series
the makloren formula is
how to take the n'th derivative from here??
where to put the formula in and get the n'th derivative??
this function
is for approximating so in order for me to get to the n'th members approximation
first i need to do manually one by one n times derivative
so its not helping me
??