Question Number 144413 by imjagoll last updated on 25/Jun/21 $$\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\left[\:\frac{\mathrm{1}}{\mathrm{4}−\mathrm{4}\sqrt{\mathrm{x}}}−\frac{\mathrm{1}}{\mathrm{5}−\mathrm{5}\sqrt[{\mathrm{5}}]{\mathrm{x}}}\:\right]\:=? \\ $$ Answered by Olaf_Thorendsen last updated on 25/Jun/21 $${f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{4}−\mathrm{4}\sqrt{{x}}}−\frac{\mathrm{1}}{\mathrm{5}−\mathrm{5}\sqrt[{\mathrm{5}}]{{x}}} \\ $$$$\mathrm{Let}\:{x}\:=\:{X}^{\mathrm{10}} \\ $$$${f}\left({X}^{\mathrm{10}}…
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Question Number 78865 by jagoll last updated on 21/Jan/20 $$ \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }\:}\:−\sqrt[{\mathrm{3}}]{\mathrm{2}}}{\mathrm{2x}^{\mathrm{3}} } \\ $$ Commented by jagoll last updated on 21/Jan/20 $$\mathrm{dear}\:\mathrm{mr}\:\mathrm{Mjs}\:.\:\mathrm{what}\:\mathrm{value}\:\mathrm{the}\:\mathrm{limit}?…
Question Number 78828 by john santu last updated on 21/Jan/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{2}+\mathrm{sin}\:{x}\right).{lnx}\:=\:? \\ $$ Commented by mr W last updated on 21/Jan/20 $$\left(\mathrm{2}+\mathrm{sin}\:{x}\right).{lnx}\:>\mathrm{ln}\:{x} \\ $$$$\underset{{x}\rightarrow\infty}…
Question Number 13276 by tawa tawa last updated on 17/May/17 Commented by tawa tawa last updated on 17/May/17 $$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{That}\:\mathrm{is}\:\mathrm{what}\:\mathrm{i}\:\mathrm{want}\:\mathrm{to}\:\mathrm{confirm}. \\ $$ Commented by mrW1 last…
Question Number 78791 by jagoll last updated on 20/Jan/20 $$ \\ $$$$ \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{2}+\mathrm{3x}−\mathrm{x}^{\mathrm{2}} }\:−\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{2}}\:? \\ $$ Answered by john santu last updated…
Question Number 13252 by raktim Ghosh last updated on 17/May/17 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}sin}\:\mathrm{x} \\ $$ Answered by Abbas-Nahi last updated on 17/May/17 $$={x}\:{li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\:\frac{\mathrm{sin}\:{x}}{{x}} \\ $$$$=\mathrm{0}\:\left(\mathrm{1}\right)\:\:;{since}\left({li}\underset{×\rightarrow\mathrm{0}}…
Question Number 78693 by TawaTawa last updated on 19/Jan/20 Commented by abdomathmax last updated on 20/Jan/20 $${let}\:{f}\left({x}\right)=\frac{\left(^{\mathrm{3}} \sqrt{{x}}\right)+\left(^{\mathrm{3}} \sqrt{{a}}\right)}{{x}+{a}}\:\:{changement}\:{x}+{a}={t}\:{give} \\ $$$${f}\left({x}\right)={g}\left({t}\right)=\frac{\left(^{\mathrm{3}} \sqrt{{t}−{a}}+\left(^{\mathrm{3}} \sqrt{{a}}\right)\right.}{{t}}\:{we}\:{hsve} \\ $$$$\alpha^{\mathrm{3}}…
Question Number 78682 by Omer Alattas last updated on 19/Jan/20 Commented by mathmax by abdo last updated on 19/Jan/20 $${we}\:{have}\:\left({sinx}\right)^{{x}} ={e}^{{xln}\left({sinx}\right)} \:\:{and}\:{xln}\left({sinx}\right)\sim{xlnx}\:\:\left({x}\rightarrow\mathrm{0}\right)\Rightarrow \\ $$$${lim}_{{x}\rightarrow\mathrm{0}^{+} }…
Question Number 144204 by bemath last updated on 23/Jun/21 $$\mathrm{Find}\:\underset{\mathrm{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{f}\left(\mathrm{2h}+\mathrm{2}+\mathrm{h}^{\mathrm{2}} \right)−\mathrm{f}\left(\mathrm{2}\right)}{\mathrm{f}\left(\mathrm{h}−\mathrm{h}^{\mathrm{2}} +\mathrm{1}\right)−\mathrm{f}\left(\mathrm{1}\right)}=? \\ $$$$\mathrm{if}\:\mathrm{given}\:\mathrm{that}\:\begin{cases}{\mathrm{f}\:'\left(\mathrm{2}\right)=\mathrm{6}}\\{\mathrm{f}\:'\left(\mathrm{1}\right)=\mathrm{4}}\end{cases} \\ $$ Answered by bramlexs22 last updated on 23/Jun/21 $$\:\underset{\mathrm{h}\rightarrow\mathrm{0}}…