Question Number 191168 by Mingma last updated on 19/Apr/23 Answered by mehdee42 last updated on 19/Apr/23 $${A}={lim}_{{n}\rightarrow\infty} \frac{\sqrt[{{n}}]{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)…\left(\mathrm{2}{n}\right)}}{{n}}={lim}_{{n}\rightarrow\infty} \sqrt[{{n}}]{\frac{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)…\left(\mathrm{2}{n}\right)}{{n}^{{n}} }} \\ $$$$\Rightarrow{lnA}={lim}_{{n}\rightarrow\infty} \:\frac{\mathrm{1}}{{n}}\left[{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)+{ln}\left(\mathrm{1}+\frac{\mathrm{2}}{{n}}\right)+…+{ln}\left(\mathrm{1}+\frac{{n}}{{n}}\right)\right] \\ $$$$={lim}_{{n}\rightarrow\infty}…
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Question Number 60007 by meme last updated on 17/May/19 $${df}\:{of}\:{f}\left({x}\right)={x}^{{x}} {y}^{{y}} \\ $$ Answered by alex041103 last updated on 18/May/19 $${if}\:{you}\:{mean}\:{f}\left({x},{y}\right)={x}^{{x}} {y}^{{y}} \:{then} \\ $$$${df}=\frac{\partial{f}}{\partial{x}}{dx}+\frac{\partial{f}}{\partial{y}}{dy}=…
Question Number 60006 by meme last updated on 17/May/19 $${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{x}^{{x}} }{{x}}=? \\ $$ Commented by maxmathsup by imad last updated on 17/May/19 $${let}\:{A}\left({x}\right)\:=\frac{{x}^{{x}} }{{x}}\:\:\:{for}\:{x}>\mathrm{0}\:\Rightarrow{A}\left({x}\right)\:=\frac{{e}^{{xln}\left({x}\right)}…
Question Number 125523 by Algoritm last updated on 11/Dec/20 Answered by Dwaipayan Shikari last updated on 11/Dec/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{2}{x}+\mathrm{3}\right){log}\left(\frac{{x}+\mathrm{2}}{{x}}\right) \\ $$$$=\left(\mathrm{2}{x}+\mathrm{3}\right)\left(\frac{\mathrm{2}}{{x}}\right)=\mathrm{4}+\frac{\mathrm{6}}{{x}}=\mathrm{4}\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{z}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{log}\left(\mathrm{1}+{z}\right)={z} \\ $$ Terms…
Question Number 59961 by bhanukumarb2@gmail.com last updated on 16/May/19 Commented by bhanukumarb2@gmail.com last updated on 16/May/19 $${i}\:{know}\:{one}\:{mthd}\:{by}\:{stirling}\:{approximation} \\ $$$${plz}\:{try}\:{any}\:{other}\:{mthd} \\ $$$${doubt}\:{we}\:{can}\:{use}\:{cesaro}\:{theoram}\:{or}\:{nt}???? \\ $$$$ \\ $$…
Question Number 190996 by cortano12 last updated on 16/Apr/23 $$\:\:\:\mathrm{If}\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{3x}}−\mathrm{3}}{\:\sqrt{\mathrm{2x}−\mathrm{4}}−\sqrt{\mathrm{2}}}\:=\:\mathrm{A} \\ $$$$\:\:\:\mathrm{and}\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{3x}}+\mathrm{x}−\mathrm{6}}{\:\sqrt{\mathrm{4x}−\mathrm{8}}+\mathrm{1}−\mathrm{x}}\:=\:\mathrm{pA} \\ $$$$\:\:\:\mathrm{then}\:\mathrm{p}\:=?\: \\ $$ Commented by mustafazaheen last updated on 16/Apr/23…
Question Number 190998 by mathlove last updated on 16/Apr/23 Commented by mr W last updated on 16/Apr/23 $${is}\:{it}\:{normal}\:{when}\:{somebody}\:{asks} \\ $$$${you}\:{directly}\:{a}\:{question}\:{but}\:{you}\:{totally} \\ $$$${irgnore}\:{it}\:{without}\:{giving}\:{any}\:{reply}? \\ $$$${i}\:{find}\:{this}\:{behaviour}\:{at}\:{least}\:{impolite}. \\…
Question Number 125394 by Mammadli last updated on 10/Dec/20 $$\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{{lim}}}\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{3}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{5}}{\mathrm{2}^{\mathrm{3}} }+…+\frac{\mathrm{2}\boldsymbol{{n}}−\mathrm{1}}{\mathrm{2}^{\boldsymbol{{n}}} }\right)=? \\ $$ Answered by Dwaipayan Shikari last updated on 10/Dec/20 $$\underset{{n}=\mathrm{1}}…
Question Number 59835 by bhanukumarb2@gmail.com last updated on 15/May/19 Answered by tanmay last updated on 15/May/19 $${T}_{{r}} =\frac{\left({cos}\mathrm{2}\theta\right)^{\mathrm{2}{r}−\mathrm{1}} }{\mathrm{2}{r}−\mathrm{1}} \\ $$$${l}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\Sigma\frac{\left({cos}\mathrm{2}\theta\right)^{\mathrm{2}{r}−\mathrm{1}} }{\mathrm{2}{r}−\mathrm{1}} \\ $$$${l}=\frac{\left({cos}\mathrm{2}\theta\right)^{\mathrm{1}}…