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 215667 by mathlove last updated on 14/Jan/25

$$\underset{x\to 1}{\lim }sec\left(\frac{\pi }{2}x\right)(arctanx-\frac{\pi }{4})=?$$

Answered by issac last updated on 14/Jan/25

$$\sec \left(\frac{\pi }{2}\right)(\arctan \left(1\right)-\frac{\pi }{4})$$

Commented by Ghisom last updated on 14/Jan/25

$$\mathrm{just}\mathrm{tell}\mathrm{us}\mathrm{the}\mathrm{value}\mathrm{of}\sec \frac{\pi }{2}$$

Commented by mathlove last updated on 14/Jan/25

$$corectansweris-\frac{1}{\pi }$$

Answered by Ghisom last updated on 14/Jan/25

$$\underset{x\to 1}{\lim }(\arctan x-\frac{\pi }{4})\sec \frac{\pi x}{2}=$$$$=\underset{x\to 1}{\lim }\frac{\arctan x-\frac{\pi }{4}}{\cos \frac{\pi x}{2}}=$$$$\left[{\mathrm{l}}^{\prime }\mathrm{H}\widehat{\mathrm{o}pital}\right]$$$$=\underset{x\to 1}{\lim }\frac{\frac{1}{x^2+1}}{-\frac{\pi }{2}\sin \frac{\pi x}{2}}=\frac{\frac{1}{2}}{-\frac{\pi }{2}}=-\frac{1}{\pi }$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com