Category: Limits

Question Number 114028 by AbhishekBasnet last updated on 16/Sep/20 Commented by bemath last updated on 17/Sep/20 $$\underset{x\to \mathrm{\infty }}{\lim }\sqrt{x^2+x}-\sqrt{x}=\frac{1-0}{2.1}=\frac{1}{2}$$ Answered by Olaf last…

Question Number 179503 by cortano1 last updated on 30/Oct/22 $$\underset{x\to 1}{\lim }(\frac{1}{{\tan }^{-1}\left(\mathrm{x}\right)-\frac{\pi }{4}}-\frac{2}{\mathrm{x}-1})=?$$ Commented by CElcedricjunior last updated on 30/Oct/22 $$\underset{x\to 1}{\lim }\left(\frac{\mathbf{x}-1-2\mathbf{arctan}\left(\mathbf{x}\right)+\mathit{\pi }/2}{(\mathbf{x}-1)(\mathbf{arctanx}-\frac{\mathit{\pi }}{4})}\right)=\frac{0}{0}=\mathbf{FI}$$$$\boldsymbol{{to}}\:\boldsymbol{{apply}}\:\boldsymbol{{hospital}}…

Question Number 179366 by mathlove last updated on 28/Oct/22 $$\underset{x\to \pi }{\lim }\frac{sin\frac{x}{2}-1}{x-\pi }=?$$ Commented by mahdipoor last updated on 28/Oct/22 $$={D}_{{x}} \left({sin}\frac{{x}}{\mathrm{2}}\right)_{{x}=\pi} =\frac{\mathrm{1}}{\mathrm{2}}{cos}\left(\frac{{x}}{\mathrm{2}}\right)_{{x}=\pi} =\mathrm{0} \…

Question Number 113742 by bemath last updated on 15/Sep/20 $$\underset{x\to 0}{\lim }\frac{{(1+x)}^{\frac{1}{x}}-e-\frac{ex}{2}}{x^2}=?$$ Answered by bobhans last updated on 15/Sep/20 $${L}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+{x}\right)^{\frac{\mathrm{1}}{{x}}} −{e}−\frac{{ex}}{\mathrm{2}}}{{x}^{\mathrm{2}}…

Question Number 113651 by bemath last updated on 14/Sep/20 $$\underset{x\to 0}{\lim }(\frac{1}{2}-\frac{1}{1+e^{-x}}).\frac{1}{3x}=?$$ Answered by john santu last updated on 14/Sep/20 $$byTaylorseries$$$${let}\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}+{e}^{−{x}}…