Category: Limits

Question Number 84568 by jagoll last updated on 14/Mar/20 $$\mathrm{without}{\mathrm{L}}^{\prime }\mathrm{hopital}$$$$\underset{x\to -\frac{1}{2}}{\lim }\frac{{2\mathrm{x}}^3+{3\mathrm{x}}^2-\sqrt{\mathrm{a}+\mathrm{bx}}}{{4\mathrm{x}}^2-1}=-\frac{3}{4}$$$$\mathrm{find}\mathrm{a}+\mathrm{b}$$ Commented by john santu last…

Question Number 84460 by jagoll last updated on 13/Mar/20 $$\underset{x\to 0}{\lim }\frac{\sin (2+\mathrm{x})-\sin (2-\mathrm{x})}{\mathrm{x}}$$ Commented by jagoll last updated on 13/Mar/20 $$\underset{x\to 0}{\lim }\frac{\cos (2+\mathrm{x})+\cos (2-\mathrm{x})}{1}$$$$=\:\mathrm{2cos}\:\mathrm{2} \…

Question Number 84377 by john santu last updated on 12/Mar/20 $$\underset{x\to 0}{\lim }\frac{\sqrt{1+\tan \mathrm{x}}-\sqrt{1+\sin \mathrm{x}}}{{\mathrm{x}}^2\sin \mathrm{x}}$$ Answered by john santu last updated on 12/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{tan}\:\mathrm{x}}+\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}}\:×\:\underset{{x}\rightarrow\mathrm{0}}…

Question Number 84364 by jagoll last updated on 12/Mar/20 $$\underset{x\to \pi }{\lim }\frac{\sqrt{\pi }-\sqrt{\pi +4\mathrm{x}}}{\cos \left(\frac{\pi (\mathrm{x}+1)}{2}\right)}=?$$ Answered by john santu last updated on 12/Mar/20 $$\sqrt{\pi }\times \underset{x\to \pi }{\lim }\frac{1-\sqrt{1+\frac{4\mathrm{x}}{\pi }}}{-\sin \left(\frac{\pi \mathrm{x}}{2}\right)}=$$$$−\sqrt{\pi}\:×\:\underset{{x}\rightarrow\pi}…

Question Number 18803 by daffa22 last updated on 30/Jul/17 Commented by daffa22 last updated on 30/Jul/17 $$\mathrm{help}$$ Answered by behi.8.3.4.1.7@gmail.com last updated on…