Question Number 54679 by Raj Singh last updated on 09/Feb/19 Commented by maxmathsup by imad last updated on 09/Feb/19 $${let}\:{f}\left({x}\right)=\frac{\mathrm{1}}{\:\sqrt{{x}+{a}}}\:\:{for}\:{x}>−{a}\:\:{we}\:{have}\:{f}^{'} \left({x}\right)={lim}_{{h}\rightarrow\mathrm{0}} \:\frac{{f}\left({x}+{h}\right)−{f}\left({x}\right)}{{h}} \\ $$$$={lim}_{{h}\rightarrow\mathrm{0}} \:\:\frac{\frac{\mathrm{1}}{\:\sqrt{{x}+{h}+{a}}\:\:}−\frac{\mathrm{1}}{\:\sqrt{{x}+{a}}}}{{h}}\:={lim}_{{h}\rightarrow\mathrm{0}}…
Question Number 119969 by huotpat last updated on 28/Oct/20 Answered by Dwaipayan Shikari last updated on 28/Oct/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{{k}^{\mathrm{2}} +{k}+\mathrm{1}} \\ $$$$\underset{{k}=\mathrm{1}}…
Question Number 119965 by sdfg last updated on 28/Oct/20 Answered by Dwaipayan Shikari last updated on 28/Oct/20 $$\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\infty} {t}^{{x}−\mathrm{1}} {e}^{−{t}} {dt} \\ $$$$\frac{{d}\Gamma\left({x}\right)}{{dx}}=\int_{\mathrm{0}} ^{\infty}…
Question Number 119937 by bobhans last updated on 28/Oct/20 $$\:\left({i}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{cos}\:\frac{\pi}{\mathrm{7}}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{cos}\:\frac{\mathrm{9}\pi}{\mathrm{7}}\right)? \\ $$$$\left({ii}\right)\:\left(\sqrt{\mathrm{3}}+\mathrm{tan}\:\mathrm{1}°\right)\left(\sqrt{\mathrm{3}}+\mathrm{tan}\:\mathrm{2}°\right)\left(\sqrt{\mathrm{3}}+\mathrm{tan}\:\mathrm{3}°\right)×…×\left(\sqrt{\mathrm{3}}+\mathrm{tan}\:\mathrm{29}°\right)? \\ $$ Answered by TANMAY PANACEA last updated on 28/Oct/20 $$\left.{ii}\right)\:\sqrt{\mathrm{3}}\:+{tan}\mathrm{1}^{{o}} \\ $$$$={tan}\mathrm{60}^{{o}}…
Question Number 185453 by cortano1 last updated on 22/Jan/23 $$\:{Find}\:{the}\:{largest}\:{possible}\:{area} \\ $$$$\:{of}\:{trapezoid}\:{that}\:{can}\:{be}\:{drawn}\: \\ $$$$\:{under}\:{the}\:{x}−{axis}\:{so}\:{that}\:{one}\: \\ $$$$\:{of}\:{its}\:{bases}\:{is}\:{on}\:{the}\:{x}−{axis}\: \\ $$$$\:{and}\:{the}\:{other}\:{two}\:{vertices}\:{are} \\ $$$$\:{on}\:{the}\:{curve}\:{y}={x}^{\mathrm{2}} −\mathrm{9}\: \\ $$ Commented by…
Question Number 119724 by benjo_mathlover last updated on 26/Oct/20 $${Let}\:{x},{y},{z}\:{be}\:{non}\:{negative}\:{real}\:{numbers} \\ $$$${such}\:{that}\:{x}+{y}+{z}=\mathrm{1}.\:{Find}\:{the}\:{extremum} \\ $$$${of}\:{F}\:=\:\mathrm{2}{x}^{\mathrm{2}} +{y}+\mathrm{3}{z}^{\mathrm{2}} \:. \\ $$ Answered by mindispower last updated on 26/Oct/20…
Question Number 119692 by bemath last updated on 26/Oct/20 $${If}\:{x}\:{is}\:{real}\:{number}\:{satisfying} \\ $$$$\mathrm{3}{x}+\frac{\mathrm{1}}{\mathrm{2}{x}}=\mathrm{4}\:,\:{find}\:{the}\:{value}\:{of} \\ $$$$\mathrm{27}{x}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{8}{x}^{\mathrm{3}} }\:. \\ $$ Commented by bemath last updated on 26/Oct/20…
Question Number 54152 by ajfour last updated on 30/Jan/19 Commented by ajfour last updated on 30/Jan/19 $${Given}\:{arc}\:{of}\:{length}\:{L}.\:{Find}\:{radius} \\ $$$${R}\:{such}\:{that}\:{segment}\:{area}\:{is}\:{a} \\ $$$$\:\:\:\:\left({i}\right){maximum}\:\:\left({ii}\right){minimum}. \\ $$ Commented by…
Question Number 54137 by ajfour last updated on 29/Jan/19 Commented by ajfour last updated on 29/Jan/19 $${Centres}\:{of}\:{two}\:{spheres}\:{of}\:{radii}\:{R}\: \\ $$$${r}\:{are}\:\mathrm{2}{a}\:{distance}\:{apart}.\:{Find}\:{a} \\ $$$${point}\:{on}\:{the}\:{circumference}\:{of}\:{the} \\ $$$${circle}\:{with}\:{AB}\:{as}\:{diameter}\:{from} \\ $$$${which}\:{maximum}\:{surface}\:{area}\:{is}…
Question Number 119565 by bemath last updated on 25/Oct/20 Commented by bemath last updated on 25/Oct/20 $${gave}\:{kudos}\: \\ $$ Answered by TANMAY PANACEA last updated…