Question Number 144513 by mnjuly1970 last updated on 26/Jun/21 Answered by Olaf_Thorendsen last updated on 26/Jun/21 $$\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{−{x}} \:=\:{e}^{−{x}\mathrm{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)} \:\underset{\infty} {\sim}\:{e}^{−{x}\left(\frac{\mathrm{1}}{{x}}−\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} }\right)} \\ $$$$\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{−{x}} \:\underset{\infty} {\sim}\:\frac{\mathrm{1}}{{e}}{e}^{\frac{\mathrm{1}}{\mathrm{2}{x}}}…
Question Number 144502 by alcohol last updated on 26/Jun/21 $${it}\:{is}\:{known}\:{that}\:{after}\:{injecting}\:{the}\:\mathrm{1}^{{st}} \\ $$$${dosage}\:{of}\:{a}\:{drug}\:{in}\:{exactly}\:{hours} \\ $$$${p}\left({t}\right)=\begin{cases}{{Ae}^{−\frac{{t}}{\mathrm{24}}} ,\:\mathrm{0}\leqslant{t}\leqslant\mathrm{8}}\\{\left({A}+{Ae}^{−\frac{\mathrm{1}}{\mathrm{3}}} \right){e}^{−\left(\frac{{t}−\mathrm{8}}{\mathrm{24}}\right)} ,\:\mathrm{8}\:\leqslant\:{t}\leqslant\mathrm{24}}\end{cases} \\ $$$${A}\:{is}\:{the}\:{initial}\:{dosage}\:{at}\:{t}=\:\mathrm{0}{hours} \\ $$$$\left.{a}\right)\:{show}\:{that}\:{towards}\:{the}\:{application}\:{of} \\ $$$${the}\:{n}^{{th}} \:{dosage}\:,\:{the}\:{dosage}\:{remained}\:{in}\:{blood}\:{is} \\…
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Question Number 144447 by pyra last updated on 25/Jun/21 Commented by Canebulok last updated on 25/Jun/21 indeterminate Answered by Dwaipayan Shikari last updated on 25/Jun/21…
Question Number 144413 by imjagoll last updated on 25/Jun/21 $$\:\:\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…