Category: Limits

Question Number 114981 by bobhans last updated on 22/Sep/20 $$Without{L}^{\prime }Hopital$$$$\left(1\right)\underset{x\to 1}{\lim }\frac{x{(x+\frac{1}{x})}^5-32}{x-1}=?$$$$\left(2\right)\underset{x\to \mathrm{\infty }}{\lim }\sqrt{2x+\sqrt{2x+\sqrt{2x+\sqrt{2x+\sqrt{\dots }}}}}-\sqrt{2x}=?$$ Commented by Dwaipayan Shikari last updated…

Question Number 180467 by mathlove last updated on 12/Nov/22 Answered by cortano1 last updated on 12/Nov/22 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 180359 by mathlove last updated on 11/Nov/22 Answered by Frix last updated on 11/Nov/22 $$\mathrm{certainly}\mathrm{you}\mathrm{do}\mathrm{not}\mathrm{mean}x!\mathrm{which}\mathrm{is}$$$$\mathrm{defined}\mathrm{for}x\in \mathbb{N}\Rightarrow \mathrm{no}\mathrm{limit}\mathrm{exists}$$$$\mathrm{but}\mathrm{you}\mathrm{mean}x!=\mathrm{\Gamma }(x+1)$$$$\mathrm{we}\mathrm{know}\mathrm{\Gamma }\left(1\right)=1$$$$\mathrm{let}\:\Gamma\left({x}+\mathrm{1}\right)={f}\left({x}\right)…

Question Number 114696 by bemath last updated on 20/Sep/20 $$\underset{x\to 0}{\lim }\frac{\sinh \left(2x\right)-\sin 2x}{x^5}=?$$ Answered by bobhans last updated on 20/Sep/20 $${e}^{\mathrm{2}{x}} =\mathrm{1}+\mathrm{2}{x}+\mathrm{2}{x}^{\mathrm{2}} +\frac{\mathrm{4}{x}^{\mathrm{3}} }{\mathrm{3}}+\frac{\mathrm{2}{x}^{\mathrm{4}}…

Question Number 114543 by bemath last updated on 19/Sep/20 $$\underset{x\to 0}{\lim }\frac{x^2\arctan \left(2x\right)}{x\cos x+\tan x}?$$ Answered by bobhans last updated on 19/Sep/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{2}} \:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{2}{x}\right)}{{x}\:\mathrm{cos}\:{x}+\mathrm{tan}\:{x}}\:=\:\underset{{x}\rightarrow\mathrm{0}}…