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Author: Tinku Tara

S-n-0-n-2-n-1-n-3-does-S-converge-

Question Number 2497 by 123456 last updated on 21/Nov/15 $$\mathrm{S}=\underset{{n}=\mathrm{0}} {\overset{+\infty} {\sum}}\frac{{n}+\mathrm{2}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{3}\right)} \\ $$$$\mathrm{does}\:\mathrm{S}\:\mathrm{converge}? \\ $$ Answered by prakash jain last updated on 21/Nov/15 $$\mathrm{S}=\underset{{n}=\mathrm{0}}…

find-dx-1-sinx-sin-2x-

Question Number 68033 by mathmax by abdo last updated on 03/Sep/19 $${find}\:\int\:\:\frac{{dx}}{\mathrm{1}+{sinx}\:+{sin}\left(\mathrm{2}{x}\right)} \\ $$ Answered by MJS last updated on 04/Sep/19 $$\mathrm{I}\:\mathrm{think}\:\mathrm{I}\:\mathrm{did}\:\mathrm{this}\:\mathrm{before} \\ $$$$\mathrm{we}\:\mathrm{have}\:\mathrm{to}\:\mathrm{use}\:\mathrm{Weierstrass} \\…

x-t-cos-t-y-t-sin-t-0-t-pi-If-z-f-x-y-is-a-curtain-with-height-of-1-what-is-the-surface-area-of-the-curtain-

Question Number 2491 by Filup last updated on 21/Nov/15 $${x}\left({t}\right)=\mathrm{cos}\:{t} \\ $$$${y}\left({t}\right)=\:\mathrm{sin}\:{t} \\ $$$$\mathrm{0}\leqslant{t}\leqslant\pi \\ $$$$ \\ $$$$\mathrm{If}:\:\:\:{z}={f}\left({x},\:{y}\right)\:\:\mathrm{is}\:\mathrm{a}\:'{curtain}'\:\mathrm{with}\:\mathrm{height}\: \\ $$$$\mathrm{of}\:\mathrm{1},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:'{curtain}'? \\ $$ Commented by Yozzi…

0-sin-1-x-1-pi-sin-pi-x-dx-

Question Number 133563 by bemath last updated on 23/Feb/21 $$\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\left[\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{x}}−\frac{\mathrm{1}}{\pi}\mathrm{sin}\:\left(\frac{\pi}{\mathrm{x}}\right)\right]\:\mathrm{dx} \\ $$ Answered by EDWIN88 last updated on 23/Feb/21 $$\:\mathrm{Calculate}\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\left(\mathrm{sin}\left(\:\frac{\mathrm{1}}{\mathrm{x}}\right)−\frac{\mathrm{1}}{\pi}\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{x}}\:\right)\:\right)\mathrm{dx} \\…

Evaluate-n-1-1-n-1-n-1-1-2-1-3-1-4-

Question Number 2489 by Filup last updated on 21/Nov/15 $$\mathrm{Evaluate}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{\:\sqrt{{n}}}\right)=\mathrm{1}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{4}}}+… \\ $$ Commented by Yozzi last updated on 21/Nov/15 $$\underset{{r}=\mathrm{1}}…