Question Number 12185 by prakash jain last updated on 15/Apr/17 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{velocity} \\ $$$${v}={K}\left({y}\hat {{i}}+{x}\hat {{j}}\right) \\ $$$${prove}\:{that} \\ $$$${y}^{\mathrm{2}} ={x}^{\mathrm{2}} +{constant} \\ $$ Answered by…
Question Number 143258 by Mathspace last updated on 12/Jun/21 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{1}} \int_{{x}} ^{{x}^{\mathrm{2}} } \:\frac{{sh}\left({xt}\right)}{{x}+{t}}{dt} \\ $$ Answered by Mathspace last updated on 13/Jun/21 $$\int_{{x}} ^{{x}^{\mathrm{2}}…
Question Number 77721 by BK last updated on 09/Jan/20 Commented by MJS last updated on 09/Jan/20 $$\left(\mathrm{1}\right)\:\mathrm{divide}\:\mathrm{by}\:\mathrm{5} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{let}\:{x}={t}−\mathrm{1} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{solve}\:\mathrm{for}\:{t} \\ $$ Terms of…
Question Number 143253 by Mathspace last updated on 12/Jun/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left({x}^{\mathrm{3}} \right)}{\mathrm{1}+{x}^{\mathrm{3}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143252 by bramlexs22 last updated on 12/Jun/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{8}{x}−\mathrm{6}{x}\:\mathrm{sin}\:{x}+\mathrm{sin}\:\mathrm{2}{x}}{{x}^{\mathrm{5}} }\:=? \\ $$ Answered by Olaf_Thorendsen last updated on 12/Jun/21 $$\frac{\mathrm{8}{x}−\mathrm{6}{x}\mathrm{sin}{x}+\mathrm{sin2}{x}}{{x}^{\mathrm{5}} }\:\underset{\mathrm{0}} {\sim}\:\frac{\mathrm{8}{x}−\mathrm{6}{x}^{\mathrm{2}} +\mathrm{2}{x}}{{x}^{\mathrm{5}}…
Question Number 143255 by Mathspace last updated on 12/Jun/21 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{sin}\left(\mathrm{1}−{cosx}\right)+\mathrm{1}−{cos}\left({sinx}\right)}{{x}^{\mathrm{2}} } \\ $$ Answered by bramlexs22 last updated on 12/Jun/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{sin}\:\left(\mathrm{1}−\mathrm{cos}\:{x}\right)}{\mathrm{1}−\mathrm{cos}\:{x}}.\left(\mathrm{1}−\mathrm{cos}\:{x}\right)+\mathrm{1}−\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)}{{x}^{\mathrm{2}} } \\…
Question Number 77716 by aliesam last updated on 09/Jan/20 $$\int{sin}\left({x}^{\mathrm{4}} \right)\:{dx} \\ $$ Commented by MJS last updated on 09/Jan/20 $$\mathrm{this}\:\mathrm{can}\:\mathrm{be}\:\mathrm{solved}\:\mathrm{using}\:\mathrm{the}\:\mathrm{incomplete} \\ $$$$\mathrm{gamma}\:\mathrm{function}.\:\mathrm{I}'\mathrm{ll}\:\mathrm{post}\:\mathrm{it}\:\mathrm{later} \\ $$…
Question Number 12181 by rish@bh last updated on 15/Apr/17 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:{xyz}\:\mathrm{is}\:\mathrm{15}/\mathrm{2}\:\mathrm{or}\:\mathrm{18}/\mathrm{5} \\ $$$$\mathrm{according}\:\mathrm{as}\:\mathrm{the}\:\mathrm{series}\:{a},{x},{y},{z},{b}\:\mathrm{are} \\ $$$$\mathrm{in}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}.\:\mathrm{or}\:\mathrm{H}.\mathrm{P}.,\:\mathrm{then}\:'{a}+{b}'\:\mathrm{equals} \\ $$$$\mathrm{where}\:{a},\:{b}\:\mathrm{are}\:+\mathrm{ve}\:\mathrm{integers}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143254 by Mathspace last updated on 12/Jun/21 $${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)} \\ $$ Answered by Olaf_Thorendsen last updated on 12/Jun/21 $${R}\left({n}\right)\:=\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)}…
Question Number 143248 by cesarL last updated on 11/Jun/21 $$\int\frac{{dx}}{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}} \\ $$ Commented by mohammad17 last updated on 11/Jun/21 $$ \\ $$$$=\int\:\frac{{dx}}{\left({x}−\mathrm{2}\right)^{\mathrm{2}} −\mathrm{3}}=\frac{\mathrm{1}}{\mathrm{3}}\int\:\frac{−{dx}}{\mathrm{1}−\left(\frac{{x}−\mathrm{2}}{\:\sqrt{\mathrm{3}}}\right)^{\mathrm{2}} }=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}{coth}^{−\mathrm{1}}…