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Question Number 160900 by LEKOUMA last updated on 08/Dec/21

$$Calculate$$$$1)\underset{x\to 0}{\lim }{\left(\frac{x+1}{2x+1}\right)}^{x^2}$$$$\underset{x\to a}{\lim }{\left(\frac{\sin x}{\sin a}\right)}^{\frac{1}{x-a}}$$

Commented by cortano last updated on 09/Dec/21

$$\left(1\right)=1$$$$\left(2\right)={\mathrm{e}}^{\underset{x\to \mathrm{a}}{\lim }\frac{\sin \mathrm{x}-\sin \mathrm{a}}{\mathrm{x}-\mathrm{a}}}={\mathrm{e}}^{\cos \mathrm{a}}$$

Commented by stelor last updated on 11/Dec/21

$$$$$$1)1$$$$2)l=\underset{x\to a}{\lim }{e}^{\frac{\ln \left(sinx\right)-ln\left(sina\right)}{x-a}}$$$$ln\left(l\right)={\left[ln\left(sinx\right)\right]}_a^{\prime }=co\tan \left(a\right)$$$$l=e^{cotan\left(a\right)}$$

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