Category: Limits

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}} \…

Question Number 195093 by Braulio last updated on 24/Jul/23 Answered by cortano12 last updated on 24/Jul/23 Answered by MM42 last updated on 24/Jul/23 $${hop}\rightarrow{lim}_{{x}\rightarrow\pi} \:\frac{\frac{\mathrm{1}}{\mathrm{2}}{cos}\frac{{x}}{\mathrm{2}}−{sinx}}{\mathrm{2}{sinxcosx}−{sinx}}…

Question Number 195065 by alcohol last updated on 23/Jul/23 Answered by Rasheed.Sindhi last updated on 23/Jul/23 $$Leta-d,a,a+darerequirednumbers$$$$(a-d)+a+(a+d)=21$$$$3a=21\Rightarrow a=7$$$$\therefore 7-d,7,7+darerequirednumbers$$$${Now}\:{by}\:{given}:\:…