Exercise
https://texercises.com/exercise/grenzwert-2/
Question
Solution
Short
Video
\(\LaTeX\)
Need help? Yes, please!
The following quantities appear in the problem:
The following formulas must be used to solve the exercise:
No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
Bestimme abcliste abc displaystylelim_xrightarrow ^+ x^x^x abc displaystylelim_nrightarrow inftynleftsqrtna-right abc displaystylelim_xrightarrow left-tan xright^cscx abcliste

Solution:
abcliste abc Es gilt x^x e^xln x + underbracexln x_rightarrow + Oxln x^. Also ist x^leftx^xright e^x^xln x e^left + underbracexln x_rightarrow + Oxln x^ln xright x underbrace e^ underbracexln x + Oxln x^_rightarrow _rightarrow lim_xrightarrow ^+ x^x^x . abc Es gilt lim_nrightarrow inftynleftsqrtna-right lim_nrightarrow infty fraca^fracn-a^fracn lim_xrightarrow + fraca^x-a^x fracmboxdmboxdx|_xa^x fracmboxdmboxdx|_xe^x ln a ln a. abc Es gilt lim_xrightarrow left-tan xright^fracsin x lim_xrightarrow +left-x+Ox^right^fracx+Ox^ lim_xrightarrow left-x+Ox^right^fracx+Ox^ lim_nrightarrowinfty left-fracn+On^-right^n underbraceleft-fracn+On^-right^Ofracn_rightarrow e^-. abcliste
Meta Information
\(\LaTeX\)-Code
Exercise:
Bestimme abcliste abc displaystylelim_xrightarrow ^+ x^x^x abc displaystylelim_nrightarrow inftynleftsqrtna-right abc displaystylelim_xrightarrow left-tan xright^cscx abcliste

Solution:
abcliste abc Es gilt x^x e^xln x + underbracexln x_rightarrow + Oxln x^. Also ist x^leftx^xright e^x^xln x e^left + underbracexln x_rightarrow + Oxln x^ln xright x underbrace e^ underbracexln x + Oxln x^_rightarrow _rightarrow lim_xrightarrow ^+ x^x^x . abc Es gilt lim_nrightarrow inftynleftsqrtna-right lim_nrightarrow infty fraca^fracn-a^fracn lim_xrightarrow + fraca^x-a^x fracmboxdmboxdx|_xa^x fracmboxdmboxdx|_xe^x ln a ln a. abc Es gilt lim_xrightarrow left-tan xright^fracsin x lim_xrightarrow +left-x+Ox^right^fracx+Ox^ lim_xrightarrow left-x+Ox^right^fracx+Ox^ lim_nrightarrowinfty left-fracn+On^-right^n underbraceleft-fracn+On^-right^Ofracn_rightarrow e^-. abcliste
Contained in these collections:
  1. Grenzwert by TeXercises
    1 | 5

Attributes & Decorations
Tags
analysis, grenzwert, limes, mathematik
Content image
Difficulty
(5, default)
Points
6 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
Creator uz
Decoration
File
Link