Question and Answers Forum

All Questions      Topic List

Limits Questions

Previous in All Question      Next in All Question      

Previous in Limits      Next in Limits      

Question Number 131052 by benjo_mathlover last updated on 01/Feb/21

$$\underset{x\to s}{\lim }\frac{x^{s^s}-s^{x^s}}{x^2-s^2}=?$$

Answered by Ar Brandon last updated on 01/Feb/21

$$\mathcal{L}=\frac{{\mathrm{s}}^{{\mathrm{s}}^{\mathrm{s}}}-{\mathrm{s}}^{{\mathrm{s}}^{\mathrm{s}}}}{{\mathrm{s}}^2-{\mathrm{s}}^2}=\frac{(\mathrm{s}-\mathrm{s})\underset{\mathrm{k}=0}{\sum ^{{\mathrm{s}}^{\mathrm{s}}-1}}{\mathrm{s}}^{{\mathrm{s}}^{\mathrm{s}}-\mathrm{k}-1}\cdot {\mathrm{s}}^{\mathrm{k}}}{(\mathrm{s}-\mathrm{s})(\mathrm{s}+\mathrm{s})}$$$$=\frac{1}{2\mathrm{s}}\underset{\mathrm{k}=0}{\sum ^{{\mathrm{s}}^{\mathrm{s}}-1}}{\mathrm{s}}^{{\mathrm{s}}^{\mathrm{s}}-1}=\frac{\left({\mathrm{s}}^{{\mathrm{s}}^{\mathrm{s}}-1}\right){\mathrm{s}}^{\mathrm{s}}}{2\mathrm{s}}$$

Commented by Ar Brandon last updated on 01/Feb/21

$${\mathrm{a}}^{\mathrm{n}}-{\mathrm{b}}^{\mathrm{n}}=(\mathrm{a}-\mathrm{b})\underset{\mathrm{k}=0}{\sum ^{\mathrm{n}-1}}{\mathrm{a}}^{\mathrm{n}-\mathrm{k}-1}{\mathrm{b}}^{\mathrm{k}}$$$$\mathrm{a}=\mathrm{s}=\mathrm{b},\mathrm{n}={\mathrm{s}}^{\mathrm{s}}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com