Question Number 92511 by Ar Brandon last updated on 07/May/20 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{x}}−\sqrt[{\mathrm{5}}]{\mathrm{x}}}{\:\sqrt[{\mathrm{3}}]{\mathrm{x}}−\sqrt[{\mathrm{4}}]{\mathrm{x}}} \\ $$ Commented by john santu last updated on 07/May/20 $$\mathrm{x}\:=\:\mathrm{t}^{\mathrm{60}} \\ $$$$\underset{\mathrm{t}\rightarrow\mathrm{0}}…
Question Number 92503 by john santu last updated on 07/May/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{e}^{\mathrm{10}{x}} −\mathrm{8}{x}\right)^{\frac{\mathrm{1}}{\mathrm{2}{x}}} \:=\: \\ $$ Commented by mathmax by abdo last updated on 07/May/20…
Question Number 158037 by Tawa11 last updated on 30/Oct/21 $$\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\underset{\mathrm{z}\rightarrow−\:\mathrm{i}} {\mathrm{lim}}\:\:\frac{\mathrm{z}\:\:\:−\:\:\:\mathrm{i}}{\mathrm{z}^{\mathrm{2}} \:\:+\:\:\:\mathrm{1}} \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:\:\underset{\mathrm{z}\rightarrow−\:\mathrm{i}} {\mathrm{lim}}\:\:\frac{\mathrm{z}\:\:\:+\:\:\:\mathrm{i}}{\mathrm{z}^{\mathrm{2}} \:\:+\:\:\:\mathrm{1}} \\ $$$$\left(\mathrm{3}\right)\:\:\:\:\:\:\:\:\:\underset{\mathrm{z}\rightarrow\mathrm{i}} {\mathrm{lim}}\:\:\frac{\mathrm{2z}^{\mathrm{2}} \:\:\:−\:\:\:\mathrm{zi}\:\:\:+\:\:\:\mathrm{1}}{\mathrm{z}\:\:−\:\:\mathrm{i}} \\ $$ Terms of Service…
Question Number 26946 by hoangnampham13 last updated on 31/Dec/17 $${f}\left({x}\right)={x}^{\mathrm{2}} {cos}\left(\frac{\mathrm{1}}{{x}}\right)\:{when}\:{x}\in\left[−\frac{\mathrm{1}}{\pi},\frac{\mathrm{1}}{\pi}\right]\backslash\left\{\mathrm{0}\right\} \\ $$$${and}\:{f}\left({x}\right)=\mathrm{0}\:{when}\:{x}=\mathrm{0}. \\ $$$$\left.{a}\right)\:{find}\:{the}\:{derivative}\:{of}\:{f}\left({x}\right)\:{on} \\ $$$${the}\:{interval}\:{of}\:\left[−\frac{\mathrm{1}}{\pi},\frac{\mathrm{1}}{\pi}\right]. \\ $$$$\left.{b}\right)\:{compute}\:{minf}\left({x}\right)\:{and}\:{maxf}\left({x}\right). \\ $$ Terms of Service Privacy…
Question Number 158017 by cortano last updated on 30/Oct/21 Commented by tounghoungko last updated on 31/Oct/21 $$\underset{{x}\rightarrow\mathrm{0}^{\:−} } {\mathrm{lim}}{f}\left({x}\right)=\:\underset{{x}\rightarrow\mathrm{0}^{\:+} } {\mathrm{lim}}{f}\left({x}\right) \\ $$$$\Rightarrow\underset{{x}\rightarrow\mathrm{0}^{\:+} } {\mathrm{lim}}\left({x}^{\frac{\mathrm{7}}{\mathrm{9}}}…
Question Number 158014 by zainaltanjung last updated on 30/Oct/21 $$ \\ $$$$ \\ $$ Answered by MathsFan last updated on 30/Oct/21 $$\mathrm{14} \\ $$ Commented…
Question Number 92423 by mhmd last updated on 06/May/20 $${lim}_{{x}\Rightarrow\infty} \frac{\mathrm{4}\left({x}+\mathrm{3}\right)!−{x}!}{{x}\left[\left({x}+\mathrm{2}\right)!−\left({x}−\mathrm{1}\right)!\right]} \\ $$ Answered by john santu last updated on 07/May/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{4}\left(\mathrm{x}+\mathrm{3}\right)\left(\mathrm{x}+\mathrm{2}\right)\left(\mathrm{x}+\mathrm{1}\right)\mathrm{x}!−\mathrm{x}!}{\mathrm{x}\left(\mathrm{x}+\mathrm{2}\right)\left(\mathrm{x}+\mathrm{1}\right)\mathrm{x}!−\mathrm{x}\left(\mathrm{x}−\mathrm{1}\right)!} \\ $$$$\underset{{x}\rightarrow\infty}…
Question Number 26877 by abdo imad last updated on 30/Dec/17 $${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\propto} \:\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)}\:\:. \\ $$ Commented by abdo imad last updated on 31/Dec/17 $${let}\:{decompose}\:{F}\left({x}\right)=\:\frac{\mathrm{1}}{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)} \\…
Question Number 157942 by mathlove last updated on 30/Oct/21 Commented by cortano last updated on 30/Oct/21 $$\left(\mathrm{1}\right){x}+\mathrm{2}{x}+\mathrm{3}{x}+…+{nx}=\frac{{n}}{\mathrm{2}}\left({nx}+{x}\right) \\ $$$$\left(\mathrm{2}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\frac{{x}}{\mathrm{2}}\right)\left(\mathrm{1}+\frac{\mathrm{2}{x}}{\mathrm{2}}\right)\left(\mathrm{1}+\frac{\mathrm{3}{x}}{\mathrm{2}}\right)…\left(\mathrm{1}+\frac{{nx}}{\mathrm{2}}\right)−\mathrm{1}}{\frac{{n}}{\mathrm{2}}\left({nx}+{x}\right)} \\ $$$${L}=\frac{\mathrm{2}}{{n}\left({n}+\mathrm{1}\right)}.\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{2}}{\mathrm{2}}+\frac{\mathrm{3}}{\mathrm{2}}+…+\frac{{n}}{\mathrm{2}}\right){x}}{{x}} \\ $$$${L}=\frac{\mathrm{2}}{{n}\left({n}+\mathrm{1}\right)}.\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+…+{n}\right)…
Question Number 92340 by jagoll last updated on 06/May/20 $$\underset{\mathrm{i}\:=\:\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\mathrm{5}^{\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{i}} } +\mathrm{3}^{\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{i}} } }{\mathrm{2}}\:=\: \\ $$ Commented by john santu last updated on…