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Category: Differentiation

Question-168244

Question Number 168244 by mnjuly1970 last updated on 07/Apr/22 Answered by MJS_new last updated on 07/Apr/22 $${x}\geqslant\mathrm{0} \\ $$$$\mathrm{rhs}\:\mathrm{is}\:\mathrm{integer}\:\Rightarrow\:\mathrm{lhs}\:\mathrm{must}\:\mathrm{be}\:\mathrm{integer} \\ $$$${x}^{\mathrm{2}} \geqslant\mathrm{0}\:\Rightarrow\:\lfloor\sqrt{{x}}\rfloor^{\mathrm{2}} +\mathrm{2}\lfloor\sqrt{{x}}\rfloor\geqslant\mathrm{2}\:\Rightarrow\:{x}\geqslant\mathrm{1} \\ $$$$\mathrm{the}\:\mathrm{only}\:\mathrm{solution}\:\mathrm{is}\:{x}=\mathrm{1}…

Question-102653

Question Number 102653 by Sontsaronald last updated on 10/Jul/20 Answered by bemath last updated on 10/Jul/20 $${y}'−{y}\mathrm{tan}\:{x}=\mathrm{sin}\:{x} \\ $$$${IF}\:{u}\left({x}\right)={e}^{−\int{tan}\:{x}\:{dx}\:} \:= \\ $$$${e}^{\mathrm{ln}\left(\mathrm{cos}{x}\right)} =\mathrm{cos}\:{x} \\ $$$${y}\left({x}\right)=\frac{\int\mathrm{cos}\:{x}\mathrm{sin}\:{x}\:{dx}\:+{C}}{\mathrm{cos}\:{x}}…

dx-5e-2x-4e-x-1-

Question Number 102461 by bemath last updated on 09/Jul/20 $$\int\:\frac{{dx}}{\:\sqrt{\mathrm{5}{e}^{\mathrm{2}{x}} +\mathrm{4}{e}^{{x}} +\mathrm{1}}}\:=? \\ $$ Answered by PRITHWISH SEN 2 last updated on 09/Jul/20 $$\int\frac{\mathrm{dx}}{\mathrm{e}^{\mathrm{x}} \sqrt{\frac{\mathrm{1}}{\mathrm{e}^{\mathrm{2x}}…

Question-167899

Question Number 167899 by peter frank last updated on 28/Mar/22 Answered by floor(10²Eta[1]) last updated on 29/Mar/22 $$\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{n}} =\mathrm{1}+\left(_{\mathrm{1}} ^{\mathrm{n}} \right)\mathrm{x}+\left(_{\mathrm{2}} ^{\mathrm{n}} \right)\mathrm{x}^{\mathrm{2}} +…+\left(_{\mathrm{r}−\mathrm{1}} ^{\mathrm{n}}…

If-x-2t-sin-2t-y-e-sin-2t-prove-that-1-y-dy-dx-tan-pi-4-t-

Question Number 102342 by bemath last updated on 08/Jul/20 $${If}\:\begin{cases}{{x}=\mathrm{2}{t}+\mathrm{sin}\:\mathrm{2}{t}}\\{{y}={e}^{\mathrm{sin}\:\mathrm{2}{t}} }\end{cases} \\ $$$${prove}\:{that}\:\frac{\mathrm{1}}{{y}}.\frac{{dy}}{{dx}}\:=\:\mathrm{tan}\:\left(\frac{\pi}{\mathrm{4}}−{t}\right) \\ $$ Commented by Dwaipayan Shikari last updated on 08/Jul/20 $${There}\:{is}\:{some}\:{error}\:{in}\:{question}\:\:{if}\:\:\:{x}=\mathrm{2}{t}−{cos}\mathrm{2}{t}\:\:{then}\:{the}\:{prove}\:{is}\:{true} \\…