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Author: Tinku Tara

secxdx-

Question Number 63976 by Scientist0000001 last updated on 11/Jul/19 $$\int{secxdx}\:\:\:\:? \\ $$ Commented by Prithwish sen last updated on 12/Jul/19 $$\int\frac{\mathrm{sec}^{\mathrm{2}} \frac{\mathrm{x}}{\mathrm{2}}}{\mathrm{1}−\mathrm{tan}^{\mathrm{2}} \frac{\mathrm{x}}{\mathrm{2}}}\mathrm{dx}\:\:\:\:\mathrm{putting}\:\mathrm{tan}\frac{\mathrm{x}}{\mathrm{2}}\:=\:\mathrm{t} \\ $$$$\mathrm{sec}^{\mathrm{2}}…

lim-x-e-xln-1-1-x-

Question Number 63964 by meme last updated on 11/Jul/19 $${li}\underset{{x}\rightarrow+\infty} {{m}e}^{−{xln}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right)} \\ $$ Commented by Prithwish sen last updated on 11/Jul/19 $$\mathrm{li}\underset{\mathrm{x}\rightarrow\infty} {\mathrm{m}}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}} \rightarrow\:\mathrm{e}^{−\mathrm{1}} \\…

Question-129496

Question Number 129496 by zakirullah last updated on 16/Jan/21 Commented by zakirullah last updated on 16/Jan/21 $$\:\:\:\:\left(\mathrm{3}^{\mathrm{2n}+\mathrm{2}} \:−\mathrm{8n}−\mathrm{9}\right)\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{64} \\ $$$$\:\:\:\:\:\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction}\:\mathrm{prove} \\ $$$$\:\:\:\:\:\:\mathrm{cos}\alpha+\mathrm{cos}\left(\alpha+\beta\right)+\mathrm{cos}\left(\alpha+\mathrm{2}\beta\right)+……….+ \\ $$$$\:\:\:\:\:\:\mathrm{cos}\left(\alpha+\left(\mathrm{n}−\mathrm{1}\right)\beta\right)=\:\mathrm{cos}\left(\alpha+\frac{\left(\mathrm{n}−\mathrm{1}\right)\beta}{\mathrm{2}}\right)×\frac{\mathrm{sin}\left(\mathrm{n}\beta/\mathrm{2}\right)}{\mathrm{sin}\left(\beta\mathrm{2}\right)} \\…

lim-x-e-xln-1-1-x-

Question Number 63959 by meme last updated on 11/Jul/19 $${li}\underset{{x}\rightarrow+\infty} {{m}e}^{{xln}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)} \\ $$ Commented by Prithwish sen last updated on 11/Jul/19 $$\:\mathrm{li}\underset{\mathrm{x}\rightarrow\infty} {\mathrm{m}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}} \rightarrow\:\mathrm{e} \\…