- #1

Lambda96

- 171

- 63

- Homework Statement
- Calculate limit of ##\frac{1}{n+1} |\frac{x-1}{\xi}|^{n+1}## as ##n \rightarrow \infty##

- Relevant Equations
- none

Hi,

I have problems with task b, more precisely with the calculation of the limit value:

By the way, I got the following for task a ##f^{(n)}(x)=(-1)^{n+1} \frac{(n-1)}{x^n}##

Unfortunately, I have no idea how to calculate the limit value for the remainder element, since ##n## appears in the exponent. I tried it with L'Hôpital's rule and then get ##\Bigl( \frac{x-1}{\xi} \Bigr)^{n+1} \log(\frac{x-1}{\xi})## and if I now form the limit, it would be ##\infty## or not?

I have problems with task b, more precisely with the calculation of the limit value:

By the way, I got the following for task a ##f^{(n)}(x)=(-1)^{n+1} \frac{(n-1)}{x^n}##

Unfortunately, I have no idea how to calculate the limit value for the remainder element, since ##n## appears in the exponent. I tried it with L'Hôpital's rule and then get ##\Bigl( \frac{x-1}{\xi} \Bigr)^{n+1} \log(\frac{x-1}{\xi})## and if I now form the limit, it would be ##\infty## or not?