Category: Limits

Question Number 195840 by NANIGOPAL last updated on 11/Aug/23 $$findthevalur$$$$li\underset{\to 0}{m}\frac{x-sinx}{x^3}$$ Commented by kokeb last updated on 11/Aug/23 $${find}\:{the}\:{valur} \…

Question Number 195619 by cortano12 last updated on 06/Aug/23 $$\cancel{\underset{―}{\underbrace{}}}$$ Answered by MM42 last updated on 06/Aug/23 $$\mathrm{\infty }$$ Answered by…

Question Number 195569 by York12 last updated on 05/Aug/23 $$a_i,b_i,x_{i}berealsfori=1,2,3,\dots ,n,suchthat$$$$\sum _{i=1}^n\left[a_i{x}_i\right]=0.Provethat$$$$\left(\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left[{x}_{{i}} ^{\mathrm{2}} \right]\right)\left(\underset{{i}=\mathrm{1}}…

Question Number 195395 by cortano12 last updated on 01/Aug/23 Answered by kapoorshah last updated on 01/Aug/23 $$Anynumberpower0is1$$$$$$$${(1+\mathrm{\infty }+\mathrm{\infty }+\dots +\mathrm{\infty })}^0=1$$ Terms…

Question Number 195325 by mathlove last updated on 30/Jul/23 $$provethat$$$$\underset{x\to \frac{\pi }{2}}{\lim }\frac{tan\left(\frac{x}{2}\right)-1}{x-\frac{\pi }{2}}=1$$ Answered by BaliramKumar last updated on 30/Jul/23 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\frac{\mathrm{d}}{\mathrm{dx}}\left({tan}\left(\frac{{x}}{\mathrm{2}}\right)−\mathrm{1}\right)}{\frac{\mathrm{d}}{\mathrm{dx}}\left({x}−\frac{\pi}{\mathrm{2}}\right)}\:=\:\frac{\mathrm{sec}^{\mathrm{2}} \left(\frac{\mathrm{x}}{\mathrm{2}}\right)\centerdot\frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{1}}…