Question Number 27097 by abdo imad last updated on 02/Jan/18 $${let}\:{give}\:\:\:{H}_{{n}} \:=\:\sum_{{k}=\mathrm{1}} ^{{n}\:\:} \:\frac{\mathrm{1}}{{k}}\:\:\:\:{for}\:{p}\:\:{fixed}\:{from}\:\mathbb{N}\: \\ $$$${find}\:\:{lim}_{{n}−>\propto} \:\:{H}_{{n}+{p}} \:\:\:−\:\:{H}_{{n}} \:\:. \\ $$ Commented by prakash jain…
Question Number 27098 by abdo imad last updated on 02/Jan/18 $${let}\:{give}\:{S}\left({x}\right)\:=\:\sum_{{n}=\mathrm{1}} ^{\propto} \frac{{x}^{{n}} }{{n}}\:\:{and}\:\:{W}\left({x}\right)=\:\:\sum_{{n}=\mathrm{1}} ^{\propto} \frac{\left(−\mathrm{1}\right)^{{n}} {x}^{{n}} }{{n}^{\mathrm{2}} } \\ $$$${calculate}\:\:\:{S}\left({x}\right).{W}\left({x}\right).\:\:\:{in}\:{that}\:{we}\:{know}\:/{x}/<\mathrm{1}. \\ $$ Commented by…
Question Number 92626 by student work last updated on 08/May/20 Commented by student work last updated on 09/May/20 $$\mathrm{who}\:\mathrm{can}\:\mathrm{solve}? \\ $$ Terms of Service Privacy…
Question Number 92577 by jagoll last updated on 08/May/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\mathrm{x}}{\mathrm{x}} \\ $$ Commented by Tony Lin last updated on 08/May/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{lnx}}{{x}} \\ $$$$=\underset{{x}\rightarrow\infty}…
Question Number 27027 by hoangnampham13 last updated on 01/Jan/18 $${Find}\:{max}\:{and}\:{min}\:{of}\:{the}\:{function}: \\ $$$${f}\left({x}\right)={x}^{\mathrm{2}} {cos}\left(\frac{\mathrm{1}}{{x}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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}}}…