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 146376 by iloveisrael last updated on 13/Jul/21

$$\underset{x\to 0}{\lim }\frac{1-\cos \mathrm{x}\cos 2\mathrm{x}\cos 3\mathrm{x}...\cos \mathrm{px}}{{\mathrm{x}}^2}=?$$

Answered by gsk2684 last updated on 13/Jul/21

$$\frac{0}{0}form,apply{L}^{\prime }Hopitalrule$$$$\underset{x\to 0}{\lim }\frac{\sin x.\cos 2x...\cos px+\cos x.\left(2\sin 2x\right)\cos 3x...\cos px+..}{2x}$$$$\frac{1}{2}(1^2+2^2+3^2+...+p^2)$$$$\frac{1}{2}.\frac{p(p+1)(2p+1)}{6}=\frac{p(p+1)(2p+1)}{12}$$

Commented by iloveisrael last updated on 13/Jul/21

$$\mathrm{wrong}$$

Commented by gsk2684 last updated on 13/Jul/21

$$edited.seetheanswer$$

Commented by iloveisrael last updated on 13/Jul/21

$$\mathrm{yes}\mathrm{correct}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com