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} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 155829 by zainaltanjung last updated on 05/Oct/21 $$\mathrm{Find}\:\mathrm{this}\:\mathrm{excercise}\:\mathrm{about}\:\mathrm{limits} \\ $$$$\mathrm{trigonometri} \\ $$$$\left.\mathrm{1}\right).\:\underset{\theta\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2cos}\:\theta−\mathrm{2}}{\mathrm{3}\theta} \\ $$$$\left.\mathrm{2}\right).\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{x}}{\mathrm{x}^{\frac{\mathrm{2}}{\mathrm{3}}} } \\ $$$$\left.\mathrm{3}\right).\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{4t}^{\mathrm{2}} +\mathrm{3t}\:\mathrm{sin}\:\mathrm{t}}{\mathrm{t}^{\mathrm{2}} } \\…
Question Number 24755 by Anoop kumar last updated on 25/Nov/17 $${Given} \\ $$$${f}\left({x}\right)\:=\underset{{x}=\mathrm{1}} {\overset{{n}} {\sum}}{tan}\left(\frac{{x}}{\mathrm{2}^{{r}} }\right).{sec}\left(\frac{{x}}{\mathrm{2}^{{r}−\mathrm{1}} }\right)\: \\ $$$$\:\:\:\:\:\:\:\:\:{where}\:{r}\:{and}\:{n}\:\varepsilon{N} \\ $$$${g}\left({x}\right)\:=\underset{{n}\rightarrow\propto} {\mathrm{li}{m}}\:\:\frac{{ln}\left({f}\left({x}\right)+{tan}\frac{{x}}{\mathrm{2}^{{n}} }\right)\:−\left({f}\left({x}\right)+{tan}\frac{{x}}{\mathrm{2}^{{n}} }\right).\left[{sin}\left({tan}\frac{{x}}{\mathrm{2}}\right)\right.}{\mathrm{1}+\left({f}\left({x}\right)\:\:+\:\:{tan}\frac{{x}}{\mathrm{2}^{{n}} }\right)^{{n}}…
Question Number 90281 by jagoll last updated on 22/Apr/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt{\mathrm{x}}}{\left(\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{x}\right)\right)^{\mathrm{2}} }\:=\:? \\ $$ Commented by jagoll last updated on 22/Apr/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{x}}}}{\mathrm{2cos}^{−\mathrm{1}} \left(\mathrm{x}\right).\left(\frac{−\mathrm{1}}{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}}…
Question Number 155812 by zainaltanjung last updated on 05/Oct/21 $$\mathrm{Use}\:\mathrm{algebraic}\:\mathrm{simplifications}\:\mathrm{to}\:\mathrm{help} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{limits},\:\mathrm{if}\:\mathrm{they}\:\mathrm{exist}. \\ $$$$\left.\mathrm{1}\right).\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{4}}{\mathrm{x}−\mathrm{2}} \\ $$$$\left.\mathrm{2}\right).\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\:\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{x}}{\mathrm{2x}^{\mathrm{2}} +\mathrm{5x}−\mathrm{7}} \\ $$$$\left.\mathrm{3}\right).\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\:\:\frac{\mathrm{3x}^{\mathrm{2}} −\mathrm{13x}−\mathrm{10}}{\mathrm{2x}^{\mathrm{2}}…
Question Number 90226 by manuel__ last updated on 22/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{x}^{\mathrm{3}} \left({e}^{{x}} −\mathrm{1}\right)−{x}^{\mathrm{2}} }{{xe}^{{x}} −{x}}\right)=? \\ $$ Commented by john santu last updated on 22/Apr/20…