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Question Number 208381 by hardmath last updated on 14/Jun/24

$$\mathrm{g}\left(\mathrm{x}\right)={\mathrm{lnx}}^2$$$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt[3]{\mathrm{x}+25}$$$$\mathrm{Find}:\underset{\mathbf{x}\to \mathbf{e}}{\lim }(\mathrm{f}\left(\mathrm{g}\left(\mathrm{x}\right)\right)=?$$

Answered by A5T last updated on 14/Jun/24

$$f\left(g\left(x\right)\right)=\sqrt[3]{ln\left(x^2\right)+25}$$$$\Rightarrow \underset{x\to e}{limf}\left(g\left(x\right)\right)=\sqrt[3]{ln\left(e^2\right)+25}=\sqrt[3]{27}=3$$

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