Question Number 39709 by Raj Singh last updated on 10/Jul/18 Commented by tanmay.chaudhury50@gmail.com last updated on 10/Jul/18 $${what}\:{is}\:{the}\:{meaning}\:{of}\:{T}^{\mathrm{3}} {T}'\:\:\: \\ $$ Answered by tanmay.chaudhury50@gmail.com last…
Question Number 39582 by Raj Singh last updated on 08/Jul/18 Answered by MrW3 last updated on 08/Jul/18 $${I}\:{think}\:{you}\:{mean}\:{tangents}\:{of}\:{the}\:{curve} \\ $$$${at}\:{positions}\:{where}\:{the}\:{curve}\:{cuts}\:{the} \\ $$$${x}−{axis}. \\ $$$${yx}^{\mathrm{2}} +{x}^{\mathrm{2}}…
Question Number 105113 by yahyajan last updated on 26/Jul/20 Answered by Dwaipayan Shikari last updated on 26/Jul/20 $$\frac{{d}}{{dx}}\left({x}!\right)={y} \\ $$$${logx}+{log}\left({x}−\mathrm{1}\right)+{log}\left({x}−\mathrm{2}\right)+….={logy} \\ $$$$\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{x}−\mathrm{1}}+….=\frac{\mathrm{1}}{{y}}\:\frac{{dy}}{{dx}} \\ $$$${x}!\left(\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{x}−\mathrm{1}}+….\right)=\frac{{dy}}{{dx}} \\…
Question Number 170579 by mnjuly1970 last updated on 27/May/22 $$ \\ $$$$\:\:\:{prove} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\mathrm{1}}{\:\:\mathrm{F}_{{n}} }\:<\:\mathrm{4}\:\:\:\:\:\:\mathrm{F}_{{n}} :\:{fibonacci}\:{sequence} \\ $$ Terms of Service…
Question Number 170566 by cortano1 last updated on 27/May/22 $$\:\:\mathrm{Find}\:\mathrm{min}\:\mathrm{value}\: \\ $$$$\:\:{f}\left({x}\right)=\:\left({x}+\mathrm{4}\right)\left({x}+\mathrm{5}\right)\left({x}+\mathrm{6}\right)\left({x}+\mathrm{7}\right) \\ $$ Answered by som(math1967) last updated on 27/May/22 $$\left({x}+\mathrm{4}\right)\left({x}+\mathrm{7}\right)\left({x}+\mathrm{5}\right)\left({x}+\mathrm{6}\right) \\ $$$$\left({x}^{\mathrm{2}} +\mathrm{11}{x}+\mathrm{28}\right)\left({x}^{\mathrm{2}}…
Question Number 39475 by Raj Singh last updated on 06/Jul/18 Answered by tanmay.chaudhury50@gmail.com last updated on 07/Jul/18 $$\:{calculatiin}\:{of}\:{slope}\:{at}\:\left({a},{b}\right)\:{w}.{r}.{t}\:\frac{{x}}{{a}}+\frac{{y}}{{b}}=\mathrm{2}\:{is} \\ $$$$\frac{\mathrm{1}}{{a}}+\frac{\frac{{dy}}{{dx}}}{{b}}=\mathrm{0} \\ $$$$\frac{{dy}}{{dx}}=−\frac{{b}}{{a}} \\ $$$${calculation}\:{of}\:{slope}\:{w}.{r}.{t}\:\frac{{x}^{{n}} }{{a}^{{n}}…
Question Number 39470 by Raj Singh last updated on 06/Jul/18 Commented by maxmathsup by imad last updated on 07/Jul/18 $${x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:=\mathrm{1}\:\Rightarrow{y}^{\mathrm{2}} =\mathrm{1}−{x}^{\mathrm{2}} \:\Rightarrow\mathrm{1}−{x}^{\mathrm{2}} \:=\mathrm{4}{x}−\mathrm{4}\:\Rightarrow{x}^{\mathrm{2}}…
Question Number 39469 by Raj Singh last updated on 06/Jul/18 Answered by tanmay.chaudhury50@gmail.com last updated on 07/Jul/18 $${let}\:{point}\:{be}\:\alpha\:,\beta \\ $$$${calculation}\:{of}\:{slope}\:{is}\: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\:\sqrt{{x}}}+\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\:\sqrt{{y}}}×\frac{{dy}}{{dx}}=\mathrm{0} \\ $$$$\frac{{dy}}{{dx}}=−\frac{\sqrt{{y}}\:}{\:\sqrt{{x}}} \\…
Question Number 39466 by Raj Singh last updated on 06/Jul/18 Commented by MJS last updated on 06/Jul/18 $${y}={x}^{\mathrm{3}} −{x}^{\mathrm{2}} \:\mathrm{has}\:\mathrm{no}\:\mathrm{vertical}\:\mathrm{tangent} \\ $$ Terms of Service…
Question Number 39457 by Raj Singh last updated on 06/Jul/18 Answered by MrW3 last updated on 06/Jul/18 $${y}={f}\left({x}\right)={b}\:{e}^{−\frac{{x}}{{a}}} \\ $$$${f}\left(\mathrm{0}\right)={b} \\ $$$${y}'={f}'\left({x}\right)=−\frac{{b}}{{a}}\:{e}^{−\frac{{x}}{{a}}} \\ $$$${f}'\left(\mathrm{0}\right)=−\frac{{b}}{{a}} \\…