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 121506 by benjo_mathlover last updated on 08/Nov/20

$$\underset{x\to 0}{\lim }{(\mathrm{x}+{\mathrm{e}}^{\frac{\mathrm{x}}{2}})}^{\frac{2}{\mathrm{x}}}?$$

Answered by liberty last updated on 09/Nov/20

$$\mathrm{L}=\underset{x\to 0}{\lim }{(\mathrm{x}+{\mathrm{e}}^{\frac{\mathrm{x}}{2}})}^{\frac{2}{\mathrm{x}}}$$$$\ln \mathrm{L}=\underset{x\to 0}{\lim }\frac{2\ln (\mathrm{x}+{\mathrm{e}}^{\frac{\mathrm{x}}{2}})}{\mathrm{x}}$$$$\ln \mathrm{L}=\underset{x\to 0}{\lim }\frac{2\left(\frac{1+\frac{1}{2}{\mathrm{e}}^{\frac{\mathrm{x}}{2}}}{\mathrm{x}+{\mathrm{e}}^{\frac{\mathrm{x}}{2}}}\right)}{1}$$$$\ln \mathrm{L}=2\left(\frac{3}{2}\right)=3\Rightarrow \mathrm{L}={\mathrm{e}}^3.▴$$$$$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com