Question Number 65773 by mathmax by abdo last updated on 03/Aug/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{1}+{x}\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right){detemine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}{\left(\mathrm{1}+{x}\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }\right)^{\mathrm{2}} }{dt} \\…
Question Number 236 by 123456 last updated on 25/Jan/15 $$\mathrm{solve} \\ $$$${y}''−{y}'−{y}={e}^{{x}} +{e}^{\mathrm{2}{x}} \\ $$$$\begin{cases}{{y}\left(\mathrm{0}\right)+{y}'\left(\mathrm{0}\right)=\mathrm{1}}\\{{y}\left(\mathrm{0}\right)−{y}'\left(\mathrm{0}\right)=\mathrm{0}}\end{cases} \\ $$ Answered by prakash jain last updated on 17/Dec/14…
Question Number 131305 by Algoritm last updated on 03/Feb/21 Answered by EDWIN88 last updated on 03/Feb/21 $$\left(\mathrm{8}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:{x}−\mathrm{cos}\:\left(\mathrm{3}{x}\right)}{\mathrm{ln}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}\:=\: \\ $$$$\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\right)−\left(\mathrm{1}−\frac{\mathrm{9}{x}^{\mathrm{2}} }{\mathrm{2}}\right)}{{x}^{\mathrm{2}} }\:=\:\mathrm{4}\:…
Question Number 65770 by mathmax by abdo last updated on 03/Aug/19 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}^{{n}} {xdx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{0}} ,{A}_{\mathrm{2}} \:{and}\:{A}_{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{A}_{{n}} {interms}\:{of}\:{n} \\ $$$$\left.\mathrm{3}\right)\:{find}\:\int_{\mathrm{0}}…
Question Number 65771 by mathmax by abdo last updated on 03/Aug/19 $${let}\:{X}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{sin}^{{n}} {xdx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{X}_{\mathrm{0}} \:,{X}_{\mathrm{1}} \:,{X}_{\mathrm{2}} ,{X}_{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{X}_{{n}} {interms}\:{of}\:{n} \\…
Question Number 65768 by mathmax by abdo last updated on 03/Aug/19 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{2}} −\mathrm{2}\left({cos}\theta\right){x}\:+\mathrm{1}} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 65769 by mathmax by abdo last updated on 03/Aug/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{2}{xcos}\theta\:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Commented by ~ À ® @ 237…
Question Number 131301 by liberty last updated on 03/Feb/21 $$\mathrm{cos}^{−\mathrm{1}} \sqrt{\mathrm{x}^{\mathrm{3}} −\mathrm{x}+\mathrm{1}}\:+\mathrm{cos}^{−\mathrm{1}} \:\sqrt{\mathrm{x}−\mathrm{x}^{\mathrm{3}} }\:+\:\mathrm{cos}^{−\mathrm{1}} \:\sqrt{\mathrm{1}−\mid\mathrm{y}\mid}\:=\:\frac{\mathrm{2}\pi}{\mathrm{3}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{y}\: \\ $$ Answered by EDWIN88 last updated on…
Question Number 65767 by mathmax by abdo last updated on 03/Aug/19 $${let}\:\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dt}}{{t}^{\mathrm{4}} +{x}^{\mathrm{4}} }\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\left({t}^{\mathrm{4}} \:+{x}^{\mathrm{4}} \right)^{\mathrm{2}} }…
Question Number 230 by ssahoo last updated on 25/Jan/15 $$\mathrm{Let}\:{z}\:\mathrm{and}\:{w}\:\mathrm{be}\:\mathrm{two}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mid{z}\mid\leqslant\mathrm{1}\:,\:\mid{w}\mid\leqslant\mathrm{1}\:\mathrm{and}\:\mid{z}+{iw}\mid=\mid{z}−{i}\overline {{w}}\mid=\mathrm{2}, \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{z}. \\ $$ Commented by 123456 last updated on 16/Dec/14 $$\mid{z}+{iw}\mid\leqslant\mid{z}\mid+\mid{w}\mid\leqslant\mathrm{2}…