Category: Limits

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}}…

Question Number 195231 by cortano12 last updated on 28/Jul/23 $$\overline{)\begin{array}{c}\cancel{\underset{―}{\underbrace{}}}\end{array}}$$ Answered by MM42 last updated on 28/Jul/23 $${lim}_{x\to 0}\sqrt{\frac{1-cos\sqrt{\pi x}}{x(1+\sqrt{cos\sqrt{\pi x}})}}$$$$={lim}_{{x}\rightarrow\mathrm{0}} \:\sqrt{\frac{\frac{\mathrm{1}}{\mathrm{2}}\pi{x}}{{x}\left(\mathrm{1}+\sqrt{\left.{cos}\sqrt{\pi{x}}\right)}\right.}}…

Question Number 195195 by Mr.D.N. last updated on 26/Jul/23 $$\mathrm{find}\mathrm{the}\mathrm{limit}:$$$$\underset{\mathrm{x}\to \mathrm{a}}{\stackrel{\lim }{}}\frac{{\mathbf{x}}^{\frac{1}{3}}}{{\mathbf{x}}^{\frac{1}{2}}}-\frac{{\mathbf{a}}^{\frac{1}{3}}}{{\mathbf{a}}^{\frac{1}{2}}}$$ Commented by Frix last updated…

Question Number 195148 by horsebrand11 last updated on 25/Jul/23 $$\overline{)\begin{array}{c}\underset{x\to 0}{\lim }\frac{1+\mathrm{x}\sin \mathrm{x}-\cos \mathrm{x}}{\sin {}^2\mathrm{x}}=?\end{array}}$$ Answered by Erico last updated on 25/Jul/23 $$\frac{\mathrm{1}+\mathrm{xsinx}−\mathrm{cosx}}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}=\frac{\mathrm{1}−\mathrm{cosx}}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}+\frac{\mathrm{x}}{\mathrm{sinx}} \…