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Question Number 114075 by bemath last updated on 17/Sep/20

Answered by john santu last updated on 17/Sep/20

$$setting\frac{1}{x}=b\wedge b\to 0$$$$\underset{b\to 0}{\lim }(\frac{1}{\sin b}-\frac{\cos b}{\sin b})=\underset{b\to 0}{\lim }\left(\frac{2\sin {}^2\left(\frac{1}{2}b\right)}{\sin b}\right)$$$$=0$$

Answered by Olaf last updated on 17/Sep/20

$$=\underset{x\to \mathrm{\infty }}{\lim }(\frac{1}{\left(\frac{1}{x}\right)}-\frac{1-\frac{1}{2}{\left(\frac{1}{x}\right)}^2}{\frac{1}{x}})$$$$=\underset{x\to \mathrm{\infty }}{\lim }(x-x+\frac{1}{2x})=0$$$$$$

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