Question Number 25221 by chernoaguero@gmail.com last updated on 06/Dec/17 $$\mathrm{Find}\:\mathrm{the}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\:\frac{\mathrm{e}^{\mathrm{x}} }{\:\sqrt{\mathrm{e}^{\mathrm{2x}} +\mathrm{1}}} \\ $$ Answered by jota+ last updated on 06/Dec/17 $$=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{1}/{e}^{{x}} \right){e}^{{x}}…
Question Number 90722 by jagoll last updated on 25/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\sqrt{\mathrm{1}+{x}}\:−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)^{\mathrm{2}} }{\mathrm{cos}\:{x}−\mathrm{1}}\:=\:? \\ $$ Commented by john santu last updated on 25/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\sqrt{\mathrm{1}+{x}}−\sqrt{\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 156250 by cortano last updated on 09/Oct/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{x}\:\sqrt{\mathrm{cos}\:\mathrm{2x}}\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{3x}}\:\sqrt[{\mathrm{4}}]{\mathrm{cos}\:\mathrm{4x}}}{\mathrm{x}^{\mathrm{2}} }\:=? \\ $$ Commented by john_santu last updated on 09/Oct/21 $${limit}=\frac{\mathrm{4}×\mathrm{5}}{\mathrm{4}}=\mathrm{5} \\ $$ Terms…
Question Number 25068 by NECx last updated on 02/Dec/17 $${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\left(\frac{{tan}\mathrm{2}{x}}{{x}−\pi/\mathrm{2}}\right) \\ $$ Answered by jota+ last updated on 03/Dec/17 $${Use}\:{Hopital}\:{rule} \\ $$$$=\frac{\underset{{x}\rightarrow\pi/\mathrm{2}}…
Question Number 156108 by cortano last updated on 08/Oct/21 $$\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{8}}} {\mathrm{lim}}\:\frac{\mathrm{1}+\mathrm{cot}\:\mathrm{6x}}{\mathrm{1}−\mathrm{sin}\:\mathrm{4x}}\:=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 25026 by NECx last updated on 02/Dec/17 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left(\frac{{x}^{\mathrm{1}/\mathrm{3}} −\mathrm{1}}{{x}^{\mathrm{1}/\mathrm{4}} −\mathrm{1}}\right) \\ $$$${Evaluate}\:{this} \\ $$$$ \\ $$ Answered by nnnavendu last updated on…
Question Number 90432 by jagoll last updated on 23/Apr/20 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\mathrm{x}\left[\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}−\mathrm{x}\:\right]\:=? \\ $$ Commented by mathmax by abdo last updated on 23/Apr/20 $${we}\:{have}\:{lim}_{{x}\rightarrow−\infty} \:{x}\:=−\infty\:\:{and}…
Question Number 155937 by cortano last updated on 06/Oct/21 $$\:\underset{\mathrm{a}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{3a}}\:\sqrt{\mathrm{cos}\:\mathrm{2a}}\:\mathrm{cos}\:\mathrm{a}}{\mathrm{a}\:\mathrm{sin}\:\mathrm{a}\:\mathrm{cos}\:\mathrm{2a}}\:=? \\ $$ Commented by john_santu last updated on 06/Oct/21 $${Limit}\:=\:\mathrm{3} \\ $$ Terms of…
Question Number 24864 by A1B1C1D1 last updated on 27/Nov/17 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{trigonometric}\:\mathrm{limit}: \\ $$$$ \\ $$$$\underset{\mathrm{x}\:\rightarrow\:\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\left(\mathrm{5tg}\left(\mathrm{x}\right)\right)\:=\: \\ $$ Answered by jota+ last updated on 28/Nov/17 $$\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 90306 by Tony Lin last updated on 22/Apr/20 $$\underset{\lambda\rightarrow\mathrm{0}} {\mathrm{lim}}\int_{\lambda} ^{\mathrm{2}\lambda} \:\frac{{e}^{−{x}} }{{x}}{dx} \\ $$ Commented by mathmax by abdo last updated on…