Category: Limits

Question Number 18593 by Joel577 last updated on 25/Jul/17 Answered by 433 last updated on 25/Jul/17 $$$$$$$$$$$$$$\frac{\mathrm{2016}\left(\frac{\mathrm{1}^{\mathrm{2015}} }{{n}^{\mathrm{2014}} }+\frac{\mathrm{2}^{\mathrm{2015}}…

Question Number 18587 by Joel577 last updated on 25/Jul/17 $$\underset{x\to 0}{\lim }\frac{x.\tan x}{x\sin x-\cos x+1}$$ Commented by Joel577 last updated on 25/Jul/17 $$\Rightarrow\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\:.\:\mathrm{tan}\:{x}}{{x}\:\mathrm{sin}\:{x}\:+\:\mathrm{2sin}^{\mathrm{2}} \:\frac{\mathrm{1}}{\mathrm{2}}{x}}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\:.\:\mathrm{tan}\:{x}}{\mathrm{sin}\:{x}\:\left({x}\:+\:\mathrm{2sin}\:\frac{\mathrm{1}}{\mathrm{2}}{x}\right)} \…

Question Number 84083 by john santu last updated on 09/Mar/20 $$\underset{\mathrm{a}\to \mathrm{x}}{\lim }\frac{(\sqrt{\mathrm{x}}-\sqrt{\mathrm{a}}-\sqrt{\mathrm{x}-\mathrm{a}})}{\sqrt{{\mathrm{x}}^2-{\mathrm{a}}^2}}=$$ Commented by mathmax by abdo last updated on 09/Mar/20…

Question Number 149547 by iloveisrael last updated on 06/Aug/21 $$\mathrm{Evaluate}\underset{x\to \frac{\pi }{7}}{\lim }\frac{8\cos \mathrm{xcos}2\mathrm{xcos}4\mathrm{x}+1}{\mathrm{x}-\frac{\pi }{7}}$$ Answered by EDWIN88 last updated on 06/Aug/21 Terms of Service Privacy Policy…

Question Number 83919 by john santu last updated on 08/Mar/20 $$\underset{x\to +\mathrm{\infty }}{\lim }{\left(\frac{3}{\pi }\mathrm{arc}\tan x\right)}^{2x}=?$$ Commented by john santu last updated on 08/Mar/20 $$=\:\mathrm{e}\:^{\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\left(\mathrm{ln}\left(\frac{\mathrm{3}}{\pi}\mathrm{tan}^{−\mathrm{1}}…