Question Number 264 by novrya last updated on 17/Dec/14 $${If}\:{f}\left(\mathrm{1}\right)=\mathrm{1}\:{and}\:{f}\:'\left({x}\right)=\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\left({f}\left({x}\right)\right)^{\mathrm{2}} }\:{then}\: \\ $$$${li}\underset{{x}\rightarrow\infty} {{m}}\:{f}\left({x}\right)=\:…. \\ $$ Commented by 123456 last updated on 17/Dec/14 $$\frac{{dy}}{{dx}}=\frac{\mathrm{1}}{{x}^{\mathrm{2}}…
Question Number 147 by novrya last updated on 25/Jan/15 $$\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\sqrt{\mathrm{9}−{y}^{\mathrm{2}} \:}\:{dydx}\:=\:…. \\ $$ Answered by vkulkarni last updated on 11/Dec/14 $$\int\sqrt{{a}^{\mathrm{2}}…
Question Number 143 by adarshkumar.9935 last updated on 25/Jan/15 $$\mathrm{tan}\:\left(\mathrm{90}−\theta\right)=? \\ $$ Answered by ganeshfrnds231 last updated on 11/Dec/14 $${sec} \\ $$ Commented by vkulkarni…
Question Number 134 by novrya last updated on 25/Jan/15 $${Solve}\:{for}\:\mathrm{3}{x}\equiv\mathrm{4}\:\left({mod}\:\mathrm{5}\right) \\ $$ Answered by rajabhay last updated on 09/Dec/14 $$\mathrm{gcd}\left(\mathrm{3},\mathrm{5}\right)=\mathrm{1}\:\mathrm{and}\:\mathrm{1}\:\mathrm{divides}\:\mathrm{4}\: \\ $$$$\mathrm{There}\:\mathrm{is}\:\mathrm{only}\:\mathrm{solution}\: \\ $$$${x}=\mathrm{3}\:\left({mod}\:\mathrm{5}\right) \\…
Question Number 137 by novrya last updated on 25/Jan/15 $${Solve}\:\mathrm{2}{x}\:\equiv\:\mathrm{6}\:\left({mod}\:\mathrm{8}\right) \\ $$ Answered by mreddy last updated on 10/Dec/14 $$\mathrm{gcd}\left(\mathrm{2},\mathrm{8}\right)=\mathrm{2},\:\mathrm{2}\:\mathrm{divides}\:\mathrm{6}\: \\ $$$$\mathrm{So}\:\mathrm{there}\:\mathrm{are}\:\mathrm{2}\:\mathrm{distinct}\:\mathrm{solutions} \\ $$$$\mathrm{Solutions}\:\mathrm{for}\:{x}\:\mathrm{are}\:\mathrm{given}\:\mathrm{by}\:\mathrm{equation} \\…
Question Number 131 by novrya last updated on 25/Jan/15 $$\int\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx}\:=…. \\ $$$$ \\ $$ Answered by rajabhay last updated on 08/Dec/14 $$\int\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}} }{dx}=\int\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}}…
Question Number 125 by novrya last updated on 25/Jan/15 $${If}\:{y}\:=\:{ln}\left(\frac{{cos}\:{x}\:+\:{sin}\:{x}}{{cos}\:{x}\:−\:{sin}\:{x}}\right)\:{then}\:\frac{{dy}}{{dx}}=…. \\ $$ Answered by sushmitak last updated on 07/Dec/14 $$\mathrm{Applying}\:\mathrm{chain}\:\mathrm{rule}\:\mathrm{and}\:\mathrm{quotient}\:\mathrm{rule}\: \\ $$$$\mathrm{for}\:\mathrm{the}\:\mathrm{cases}\:\mathrm{when}\:\mathrm{cos}\:{x}−\mathrm{sin}\:{x}\:\neq\mathrm{0}\:\mathrm{and} \\ $$$$\frac{\mathrm{cos}\:{x}+\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}>\mathrm{0}. \\…
Question Number 123 by novrya last updated on 25/Jan/15 $${Solve}\:{the}\:{differential}\:{equation}: \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }−\mathrm{2}\frac{{dy}}{{dx}}+{y}={e}^{\mathrm{4}{x}} \\ $$ Answered by sudhanshur last updated on 07/Dec/14 $$\mathrm{Let}\:{y}={Ae}^{\mathrm{4}{x}} \:…
Question Number 124 by novrya last updated on 25/Jan/15 $${If}\:{C}\:{is}\:{circle}\:\mid{z}\mid=\mathrm{1}.\:{Then}\:{the}\:{value}\:{of} \\ $$$$\underset{{C}} {\int}\:\frac{{cos}\:{z}}{{sin}\:{z}}\:{dz}\:=…. \\ $$ Commented by 123456 last updated on 13/Dec/14 $$\mathrm{o}\:\mathrm{teorema}\:\mathrm{dos}\:\mathrm{residuos}\:\mathrm{seria}\:\mathrm{bem}\:\mathrm{util}\:\mathrm{aqui}. \\ $$$$\mathrm{note}\:\mathrm{que}\:\mathrm{no}\:\mathrm{interior}\:\mathrm{do}\:\mathrm{contorno}\:\mathrm{C}\:\mathrm{so}\:\mathrm{a}\:\mathrm{um}\:\mathrm{polo}\:\mathrm{simples}\left(\mathrm{z}=\mathrm{0}\right)…
Question Number 120 by novrya last updated on 25/Jan/15 $${Evaluate}\:\int{tan}\:\theta\:{d}\theta \\ $$ Answered by ssahoo last updated on 06/Dec/14 $$\int\mathrm{tan}\:\theta\:\:{d}\theta \\ $$$$=\int\frac{\mathrm{sin}\:\theta}{\mathrm{cos}\:\theta}{d}\theta \\ $$$$\mathrm{substituting}\:\mathrm{cos}\:\theta={y} \\…