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Question Number 140530 by liberty last updated on 09/May/21

$$\underset{x\to 0}{\lim }\frac{(\mathrm{x}+\mathrm{y})\sec (\mathrm{x}+\mathrm{y})-\mathrm{ysec}\mathrm{y}}{\mathrm{x}}=?$$

Answered by EDWIN88 last updated on 09/May/21

$${\mathrm{L}}^{\prime }\mathrm{H}\ddot{\mathrm{o}pital}$$$$\underset{x\to 0}{\lim }\frac{\sec (\mathrm{x}+\mathrm{y})+(\mathrm{x}+\mathrm{y})\sec (\mathrm{x}+\mathrm{y})\tan (\mathrm{x}+\mathrm{y})-0}{1}$$$$=\underset{x\to 0}{\lim }((\mathrm{x}+\mathrm{y})\tan (\mathrm{x}+\mathrm{y})+1)\sec (\mathrm{x}+\mathrm{y})$$$$=(\mathrm{y}\tan \mathrm{y}+1)\sec \mathrm{y}$$

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