Question Number 120016 by aurpeyz last updated on 28/Oct/20 Answered by mr W last updated on 28/Oct/20 $${S}=\frac{\left(\mathrm{1}+{x}\right)^{\mathrm{16}} −\left(\mathrm{1}+{x}\right)^{\mathrm{6}} }{{x}} \\ $$$${C}_{\mathrm{7}} ^{\mathrm{16}} ={C}_{\mathrm{9}} ^{\mathrm{16}}…
Question Number 185555 by yaslm last updated on 23/Jan/23 Answered by SEKRET last updated on 24/Jan/23 $$\:\:\:\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{a}}\centerdot\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{t}}\right)\:\:\:\:\:\boldsymbol{\mathrm{x}}=\boldsymbol{\mathrm{a}}\centerdot\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{t}}\right)\:\:\:\mid_{\left(\boldsymbol{\mathrm{x}},\boldsymbol{\mathrm{y}}\right)\rightarrow\mathrm{0}} \rightarrow\mid_{\boldsymbol{\mathrm{a}}\rightarrow\mathrm{0}} \\ $$$$\:\:\boldsymbol{\mathrm{lim}}_{\boldsymbol{\mathrm{a}}\rightarrow\mathrm{0}} \:\:\frac{\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{t}}\right)}{\boldsymbol{\mathrm{a}}^{\mathrm{2}} \centerdot\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{t}}\right)+\mathrm{1}}=\boldsymbol{\mathrm{lim}}_{\boldsymbol{\mathrm{a}}\rightarrow\mathrm{0}} \frac{\mathrm{a}\centerdot\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{t}}\right)}{\boldsymbol{\mathrm{a}}^{\mathrm{2}} \centerdot\boldsymbol{\mathrm{sin}}^{\mathrm{2}}…
Question Number 120008 by help last updated on 28/Oct/20 Commented by TANMAY PANACEA last updated on 28/Oct/20 $${is}\:{the}\:{first}\left[{brackdt}\:{term}\:{contains}\:\:\boldsymbol{{x}}^{\mathrm{2}} \right. \\ $$$$ \\ $$ Commented by…
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Question Number 54460 by Azmal sheikh last updated on 03/Feb/19 $${Solve}\:\frac{{dy}}{{dx}}+\mathrm{3}{x}=\mathrm{5} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 03/Feb/19 $$\frac{{dy}}{{dx}}=\mathrm{5}−\mathrm{3}{x} \\ $$$${dy}=\left(\mathrm{5}−\mathrm{3}{x}\right){dx} \\ $$$$\int{dy}=\int\left(\mathrm{5}−\mathrm{3}{x}\right){dx}…
Question Number 185526 by Matica last updated on 23/Jan/23 $$\:{solve}\:{y}''\:=\:\left(\mathrm{2}{y}+\mathrm{3}\right)\left({y}'\right)^{\mathrm{2}} \\ $$$$ \\ $$ Answered by mr W last updated on 23/Jan/23 $${y}''={y}'\frac{{dy}'}{{dy}} \\ $$$${y}'\frac{{dy}'}{{dy}}=\left(\mathrm{2}{y}+\mathrm{3}\right)\left({y}'\right)^{\mathrm{2}}…
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Question Number 185472 by liuxinnan last updated on 22/Jan/23 $${if}\:\omega^{\mathrm{7}} =\mathrm{1} \\ $$$$\frac{\mathrm{1}}{\omega+\omega^{\mathrm{6}} }+\frac{\mathrm{1}}{\omega^{\mathrm{2}} +\omega^{\mathrm{5}} }+\frac{\mathrm{1}}{\omega^{\mathrm{3}} +\omega^{\mathrm{4}} }=? \\ $$ Commented by Shrinava last updated…
Question Number 185471 by liuxinnan last updated on 22/Jan/23 $$\int_{\:\mathrm{0}} ^{\:{r}} \frac{\mathrm{1}}{\:\sqrt{{r}^{\mathrm{2}} −{x}^{\mathrm{2}} }}{dx}=? \\ $$ Answered by hmr last updated on 22/Jan/23 $$=\:\left[{sin}^{−\mathrm{1}} \:\left(\frac{{x}}{{r}}\right)\underset{\:\:\mathrm{0}}…
Question Number 119915 by Khalmohmmad last updated on 28/Oct/20 Answered by malwaan last updated on 28/Oct/20 $$\int{x}^{\mathrm{2}} \left(\mathrm{1}\:+\:\mathrm{4}{x}^{\mathrm{3}} \:\right){dx} \\ $$$$=\int\left({x}^{\mathrm{2}} +\:\mathrm{4}{x}^{\mathrm{5}} \right){dx} \\ $$$$=\:\frac{{x}^{\mathrm{3}}…