Question Number 4487 by Rasheed Soomro last updated on 31/Jan/16 $${If}\:\:{y}^{\mathrm{2}} +\mathrm{3}{uy}−\mathrm{5}{u}^{\mathrm{2}} =\mathrm{2}\:,\:\:\mathrm{2}{t}^{\mathrm{2}} −\mathrm{2}{tu}−\mathrm{3}{u}^{\mathrm{2}} −\mathrm{1}=\mathrm{0}\: \\ $$$${and}\:\mathrm{5}{x}^{\mathrm{2}} +\mathrm{4}{xt}−{t}^{\mathrm{2}} =\mathrm{0}\:,{find}\:\:\frac{{dy}}{{dx}}\:\:{and}\:\:\:\frac{{du}}{{dt}}\:. \\ $$ Answered by Yozzii last…
Question Number 4363 by Rasheed Soomro last updated on 13/Jan/16 $${If}\:\:\underset{{x}\rightarrow{a}} {{lim}}\:\:\frac{{f}\left({x}\right)}{{g}\left({x}\right)}\:{exists}\:{and}\:\underset{{x}\rightarrow{a}} {{lim}}\:{g}\left({x}\right)=\mathrm{0}, \\ $$$${then}\:{show}\:{that} \\ $$$$\underset{{x}\rightarrow{a}} {{lim}}\:{f}\left({x}\right)=\mathrm{0}. \\ $$ Answered by Yozzii last updated…
Question Number 135342 by Algoritm last updated on 12/Mar/21 Commented by Algoritm last updated on 12/Mar/21 $$\frac{\mathrm{d}^{\mathrm{n}} \left(\mathrm{y}\right)}{\mathrm{dx}^{\mathrm{n}} }=? \\ $$ Answered by Ñï= last…
Question Number 135313 by bobhans last updated on 12/Mar/21 $${Given}\:{f}\left({x}\right)\:=\:\mathrm{5}{x}+\mathrm{cos}\:\left(\mathrm{3}{x}\right) \\ $$$${Find}\:{the}\:{value}\:{of}\:\frac{{d}}{{dx}}\:\left[{f}^{−\mathrm{1}} \left(\mathrm{1}\right)\right] \\ $$ Answered by liberty last updated on 12/Mar/21 $$\left(\mathrm{1}\right){f}\left(\mathrm{0}\right)=\mathrm{1}\Leftrightarrow{f}^{−\mathrm{1}} \left(\mathrm{1}\right)=\mathrm{0} \\…
Question Number 135309 by mnjuly1970 last updated on 12/Mar/21 $$\:\:\:\:\:\:\:\:\:\:….\:\:\mathscr{N}{ice}\:\:\:\:\mathscr{C}{alculus}\:…. \\ $$$$\:\:\:\:\:\:\:\:{prove}\:\:{that}\:::: \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({ksin}\alpha\right){x}}{\:\sqrt{{x}}}{dx}=\sqrt{\frac{\pi}{{k}}}\:{sin}\left(\frac{\alpha}{\mathrm{2}}\right)… \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\: \\ $$ Answered by mathmax…
Question Number 135308 by bobhans last updated on 12/Mar/21 Commented by mr W last updated on 12/Mar/21 $${at}\:{t}=\mathrm{3}\:{s},\:{the}\:{height}\:{is}\:\mathrm{71}.\mathrm{65}{m} \\ $$$${at}\:{t}=\mathrm{7}.\mathrm{8009}{s},\:{the}\:{ball}\:{hits}\:{the}\:{ground} \\ $$$${max}.\:{height}\:{is}\:\mathrm{75}.\mathrm{4235}{m} \\ $$$${in}\:\mathrm{6}.\mathrm{1554}−\mathrm{1}.\mathrm{5997}=\mathrm{4}.\mathrm{5557}{s}\:{the}\:{ball} \\…
Question Number 135252 by mnjuly1970 last updated on 11/Mar/21 $$\:\:\:\:\:\:\:\:\:….{advanced}\:\:\:\:{calculus}…. \\ $$$$\:\:\:\:{first}\:{prove}\:{that}::\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}_{\mathrm{1}} =\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}\right){ln}\left(\mathrm{1}+{x}\right)}{{x}}{dx}=\frac{−\mathrm{5}}{\mathrm{8}}\:\zeta\left(\mathrm{3}\right) \\ $$$$\:\:\:\:\:{then}\:{conclude}\:{that}:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}_{\mathrm{2}} =\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left(\mathrm{1}+{x}\right)}{{x}}{dx}=\frac{\zeta\left(\mathrm{3}\right)}{\mathrm{4}}…
Question Number 69680 by 20190927 last updated on 26/Sep/19 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{sinx}} \:\:,\:\mathrm{0}<\mathrm{x}<\frac{\pi}{\mathrm{2}}\:\:\:\mathrm{find}\:\mathrm{f}'\left(\mathrm{x}\right) \\ $$ Answered by MJS last updated on 26/Sep/19 $$\frac{{d}}{{dx}}\left[{u}^{{v}} \right]={u}^{{v}} \left(\frac{{u}'{v}}{{u}}+{v}'\mathrm{ln}\:{u}\right) \\ $$$$\Rightarrow…
Question Number 135211 by benjo_mathlover last updated on 11/Mar/21 $$\mathrm{Find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{4x}^{\mathrm{2}} +\mathrm{8x}+\mathrm{13}}{\mathrm{6}\left(\mathrm{1}+\mathrm{x}\right)} \\ $$ Commented by mr W last updated on 11/Mar/21 $$\underset{{x}\rightarrow−\mathrm{1}^{−} }…
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