lim-x-0-1-x-tan-pi-2-x-

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Question Number 131181 by john_santu last updated on 02/Feb/21

$$\underset{x\to 0}{\lim }(\frac{1}{x}-\tan (\frac{\pi }{2}-x))=?$$

Answered by Ar Brandon last updated on 02/Feb/21

$$\mathcal{L}=\underset{\mathrm{x}\to 0}{\lim }(\frac{1}{x}-\tan (\frac{\pi }{2}-x))=\underset{\mathrm{x}\to 0}{\lim }(\frac{1}{\mathrm{x}}-\mathrm{cotx})$$$$=\underset{\mathrm{x}\to 0}{\lim }\left\{\frac{1-\mathrm{xcotx}}{\mathrm{x}}\right\}=\underset{\mathrm{x}\to 0}{\lim }\left\{\frac{1-\mathrm{cosx}}{\mathrm{x}}\right\}=0$$

Answered by john_santu last updated on 02/Feb/21

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