Question Number 65052 by AnjanDey last updated on 24/Jul/19 $${A}.\mathrm{Evaluate}: \\ $$$$\left(\mathrm{i}\right)\int\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{9}+\mathrm{16sin}\:\mathrm{2}{x}}{dx} \\ $$$$\left(\mathrm{ii}\right)\int\frac{\mathrm{1}+{x}^{\mathrm{2}} }{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}+{x}^{\mathrm{2}} +{x}^{\mathrm{4}} }}{dx} \\ $$$$\left(\mathrm{iii}\right)\int\frac{{x}−\mathrm{1}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{3}} +{x}+{x}^{\mathrm{2}} }}{dx} \\ $$ Answered…
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Question Number 130582 by bramlexs22 last updated on 27/Jan/21 $$\mathrm{A}\:\mathrm{metal}\:\mathrm{rain}\:\mathrm{gutter}\:\mathrm{is}\:\mathrm{to}\:\mathrm{have}\:\mathrm{3}−\mathrm{inch}\:\mathrm{and} \\ $$$$\mathrm{a}\:\mathrm{3}−\mathrm{inch}\:\mathrm{bottom}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{making}\:\mathrm{an}\:\mathrm{equal} \\ $$$$\mathrm{angle}\:\theta\:\mathrm{with}\:\mathrm{the}\:\mathrm{bottom}.\:\mathrm{What}\:\mathrm{should}\: \\ $$$$\theta\:\mathrm{be}\:\mathrm{in}\:\mathrm{order}\:\mathrm{to}\:\mathrm{maximize}\:\mathrm{carrying}\:\mathrm{capasity} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{gutter}\:? \\ $$ Answered by EDWIN88 last updated…
Question Number 130580 by bramlexs22 last updated on 27/Jan/21 $$\mathrm{If}\:\mathrm{x}\epsilon\:\left[−\mathrm{1},\:\mathrm{0}\right)\:\mathrm{then}\:\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{2x}^{\mathrm{2}} −\mathrm{1}\right)−\mathrm{2sin}^{−\mathrm{1}} \left(\mathrm{x}\right)=? \\ $$ Commented by EDWIN88 last updated on 27/Jan/21 $$\pi \\ $$…
Question Number 130581 by bramlexs22 last updated on 27/Jan/21 $$\mathrm{If}\:\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} \:,\mathrm{a}_{\mathrm{3}} \:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}\:\mathrm{and}\:\mathrm{d}\:\mathrm{is}\:\mathrm{the}\:\mathrm{common} \\ $$$$\mathrm{difference}\:\mathrm{then}\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{d}}{\mathrm{1}+\mathrm{a}_{\mathrm{1}} \mathrm{a}_{\mathrm{2}} }\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{d}}{\mathrm{1}+\mathrm{a}_{\mathrm{2}} \mathrm{a}_{\mathrm{3}} }\right)=? \\ $$ Answered by…
Question Number 65044 by mathmax by abdo last updated on 24/Jul/19 $$\left.{solve}\:{x}^{\mathrm{2}} {y}^{''} \:+{xy}^{'} \:+{y}\:=\mathrm{0}\:\:{on}\:\right]\mathrm{0},+\infty\left[\:\:\:\left({put}\:{x}\:={e}^{{t}} \right)\right. \\ $$ Commented by mathmax by abdo last updated…
Question Number 65040 by aliesam last updated on 24/Jul/19 $${what}\:{is}\:{the}\:{curve}\:{of}\:{the}\:{curve}\:{caused}\:\:{by} \\ $$$${the}\:{earth}\:{to}\:{the}\:{space}\:{time}\:\_\:{fabric} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 130560 by rs4089 last updated on 26/Jan/21 Answered by Dwaipayan Shikari last updated on 26/Jan/21 $$\frac{\pi}{\mathrm{2}\left({r}+{r}^{\mathrm{3}} +{r}^{\mathrm{6}} +{r}^{\mathrm{10}} +….\right)} \\ $$ Answered by…
Question Number 130559 by Ar Brandon last updated on 26/Jan/21 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\mathrm{2xsin}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)−\mathrm{cos}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\right\} \\ $$ Answered by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{no}\:\mathrm{limit} \\…