Question Number 124244 by bramlexs22 last updated on 02/Dec/20 $${Find}\:\frac{{dy}}{{dx}}\:{of}\:{function}\:{y}=\mathrm{5}^{\sqrt{{x}}} \\ $$$${by}\:{first}\:{principle}. \\ $$ Answered by liberty last updated on 02/Dec/20 Terms of Service Privacy…
Question Number 124169 by bramlexs22 last updated on 01/Dec/20 $${A}\:{long}\:{strip}\:{of}\:{sheet}\:{metal}\:\mathrm{12}\:{inches} \\ $$$${wide}\:{is}\:{to}\:{be}\:{made}\:{into}\:{a}\:{small}\: \\ $$$${trough}\:{by}\:{turning}\:{up}\:{two}\: \\ $$$${sides}\:{at}\:{right}\:{angles}\:{to}\:{the}\:{base}\: \\ $$$${If}\:{trough}\:{is}\:{to}\:{have}\:{maximum} \\ $$$${capasit}\bar {{y}},\:{how}\:{many}\:{inches}\:{should}\:{be} \\ $$$${turned}\:{up}\:{on}\:{each}\:{side}?\: \\ $$$$\left({a}\right)\:\mathrm{6}\:{in}\:\:\:\:\left({b}\right)\:\mathrm{4}\:{in}\:{on}\:{one}\:{side},\:\mathrm{5}\:{in}\:{on}\:{the}\:{other}…
Question Number 124133 by bramlexs22 last updated on 01/Dec/20 $${Given}\:{equation}\:{of}\:{tangent}\:{line} \\ $$$${of}\:{the}\:{curve}\:{y}\:=\:\frac{{b}}{{x}^{\mathrm{2}} }\:{at}\:{point}\:\left({x},{y}\right) \\ $$$${is}\:{bx}−\mathrm{4}{y}=−\mathrm{21}.\:{The}\:{value}\:{of}\:{b}\:=? \\ $$ Answered by mr W last updated on 01/Dec/20…
Question Number 124064 by mnjuly1970 last updated on 30/Nov/20 $$\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:{prove}\:\:\:{that}::: \\ $$$$\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \left\{\frac{\mathrm{1}+\left(\mathrm{1}−{x}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} }{{x}}\:+\frac{\mathrm{2}}{{ln}\left(\mathrm{1}−{x}\right)}\right\}{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\overset{???} {=}\mathrm{2}\left(\gamma−\mathrm{1}+{log}\left(\mathrm{2}\right)\right) \\ $$ Answered by mindispower…
Question Number 124007 by liberty last updated on 30/Nov/20 $$\:{Given}\:{a}\:{function}\:{y}={f}\left({x}\right)\:{where}\:{f}^{−\mathrm{1}} \left(\frac{{x}+\mathrm{5}}{{x}−\mathrm{5}}\right)=\frac{\mathrm{8}}{{x}+\mathrm{5}} \\ $$$${Find}\:{slope}\:{of}\:{the}\:{curve}\:{y}={f}\left({x}\right)\:{at}\:{x}=\mathrm{1}\:. \\ $$ Answered by john_santu last updated on 30/Nov/20 $${f}^{−\mathrm{1}} \left(\frac{{x}+\mathrm{5}}{{x}−\mathrm{5}}\right)=\frac{\mathrm{8}}{{x}+\mathrm{5}}\:\Leftrightarrow\:{f}\left(\frac{\mathrm{8}}{{x}+\mathrm{5}}\right)=\frac{{x}+\mathrm{5}}{{x}−\mathrm{5}} \\…
Question Number 123961 by mnjuly1970 last updated on 29/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:{calculus}… \\ $$$$\:\:{prove}\:\:{that}:: \\ $$$$ \\ $$$$\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\infty} \left(\frac{{x}^{\varphi} }{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{4}\varphi} +{x}^{\mathrm{4}} }}\right){dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\overset{???} {=}\:\frac{\varphi\Gamma^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\:\sqrt{\pi}}…
Question Number 123898 by mnjuly1970 last updated on 29/Nov/20 $$\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{calculus}… \\ $$$$\:\:{find}\:\:{a}\:{series}\:{representation} \\ $$$$\:{for}\:\:{the}\:{following}\:{integral}\::: \\ $$$$\:\:\:\:\phi=\int_{\mathrm{0}} ^{\:\mathrm{1}} {cos}\left({h}\left({xln}\left({x}\right)\right){dx}\right. \\ $$$$ \\ $$ Answered by mindispower…
Question Number 123817 by benjo_mathlover last updated on 28/Nov/20 $${Among}\:{all}\:{triangles}\:{in}\:{the}\:{first} \\ $$$${quadrant}\:{formed}\:{by}\:{the}\:{x}−{axis}, \\ $$$${the}\:{y}−{axis}\:{and}\:{tangent}\:{lines}\:{to} \\ $$$${the}\:{graph}\:{of}\:{y}\:=\:\mathrm{3}{x}−{x}^{\mathrm{2}} ,\:{what}\:{is} \\ $$$${the}\:{smallest}\:{possible}\:{area}? \\ $$ Answered by MJS_new last…
Question Number 123812 by benjo_mathlover last updated on 28/Nov/20 $${Within}\:{the}\:{interval}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}\pi\:,{find}\: \\ $$$${the}\:{critical}\:{points}\:{of}\: \\ $$$${f}\left({x}\right)=\:\mathrm{sin}\:^{\mathrm{2}} {x}−\mathrm{sin}\:{x}−\mathrm{1}\:.\:{Identify} \\ $$$${the}\:{open}\:{interval}\:{on}\:{which}\:{f}\:{is}\: \\ $$$${increasing}\:{and}\:{decreasing}\:.\:{Find} \\ $$$${the}\:{function}'{s}\:{local}\:{and}\:{absolute} \\ $$$${extreme}\:{values}. \\ $$…
Question Number 123813 by snipers237 last updated on 28/Nov/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:^{{x}} \sqrt{\frac{\mathrm{1}}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{{x}} }\:\:=\:\:^{{n}} \sqrt{{n}!}\: \\ $$ Answered by Dwaipayan Shikari last updated on…