Category: Limits

Question Number 28151 by tawa tawa last updated on 21/Jan/18 $$\underset{x\to 1}{\lim }(\frac{1}{{\log }_{\mathrm{e}}\mathrm{x}}-\frac{\mathrm{x}}{\mathrm{x}-1})$$ Commented by çhëý böý last updated on 21/Jan/18 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\left(\frac{\left({x}−\mathrm{1}\right)−{xlnx}}{\left({x}−\mathrm{1}\right){lnx}}\right)=\frac{\mathrm{0}}{\mathrm{0}}…

Question Number 93676 by john santu last updated on 14/May/20 $$\mathrm{solve}\mathrm{without}{\mathrm{L}}^{\prime }\mathrm{Hopital}$$$$\underset{x\to 0}{\lim }\frac{5\sqrt{\mathrm{x}+1}-2\sqrt{\mathrm{x}+4}-1}{\mathrm{x}}?$$ Commented by mathmax by abdo last updated on 14/May/20…

Question Number 28098 by tawa tawa last updated on 20/Jan/18 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{{\log }_{\mathrm{e}}\mathrm{x}}{{\mathrm{x}}^{\mathrm{h}}},\mathrm{h}>0$$ Answered by ajfour last updated on 20/Jan/18 $$=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{1}/{x}\right)}{{hx}^{{h}−\mathrm{1}}…

Question Number 28096 by tawa tawa last updated on 20/Jan/18 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{{\mathrm{x}}^2}{\mathrm{x}-\mathrm{sinx}}$$ Commented by abdo imad last updated on 20/Jan/18 $$=\:{lim}_{{x}\rightarrow\propto\:\:} \:\:\frac{{x}}{\mathrm{1}−\frac{{sinx}}{{x}}}\:\:\:{but}\:\:\:/\frac{{sinx}}{{x}}/\leqslant\:\:\:\frac{\mathrm{1}}{/{x}/}\:_{{x}\rightarrow\propto}…

Question Number 28095 by tawa tawa last updated on 20/Jan/18 $$\underset{x\to 0^{-}}{\lim }{(1+\mathrm{tanx})}^{-\mathrm{cotx}}$$ Commented by abdo imad last updated on 20/Jan/18 $$=\:{lim}_{{x}\rightarrow\mathrm{0}^{−} }…