Question and Answers Forum

All Questions      Topic List

Limits Questions

Previous in All Question      Next in All Question      

Previous in Limits      Next in Limits      

Question Number 132079 by liberty last updated on 11/Feb/21

$$\mathrm{If}\mathrm{L}=\underset{x\to \pi /4}{\lim }\frac{\tan {}^3\mathrm{x}-\tan \mathrm{x}}{\cos (\mathrm{x}+\frac{\pi }{4})}$$$$\mathrm{then}\frac{\mathrm{L}}{4}=?$$

Answered by EDWIN88 last updated on 11/Feb/21

$$\mathrm{L}=\underset{x\to \pi /4}{\lim }\frac{\tan \mathrm{x}(\tan \mathrm{x}+1)(\tan \mathrm{x}-1)}{\cos (\mathrm{x}+\frac{\pi }{4})}$$$$\mathrm{L}=1\times 2\times \underset{x\to \pi /4}{\lim }\left(\frac{\sin \mathrm{x}-\cos \mathrm{x}}{\cos \mathrm{x}}\right).\left(\frac{1}{\cos (\mathrm{x}+\frac{\pi }{4})}\right)$$$$\mathrm{L}=-1\times 4\times \underset{x\to \pi /4}{\lim }\frac{\frac{1}{\sqrt{2}}\cos \mathrm{x}-\frac{1}{\sqrt{2}}\sin \mathrm{x}}{\cos (\mathrm{x}+\frac{\pi }{4})}$$$$\mathrm{L}=-4\times \underset{x\to \pi /4}{\lim }\frac{\cos (\mathrm{x}+\frac{\pi }{4})}{\cos (\mathrm{x}+\frac{\pi }{4})}=-4$$$$\mathrm{then}\frac{\mathrm{L}}{4}=-1$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com