Question Number 144214 by Mathspace last updated on 23/Jun/21 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{4}\pi} \:\:\frac{{sinx}}{\left(\mathrm{3}+{cosx}\right)^{\mathrm{2}} }{dx} \\ $$ Answered by bemath last updated on 23/Jun/21 $$=−\underset{\mathrm{0}} {\overset{\mathrm{4}\pi} {\int}}\:\frac{\mathrm{d}\left(\mathrm{3}+\mathrm{cos}\:\mathrm{x}\right)}{\left(\mathrm{3}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}}…
Question Number 144211 by Mathspace last updated on 23/Jun/21 $${find}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{4}} +\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 78667 by berket last updated on 19/Jan/20 $${let}\:{f}\left({x}\right)=\left({x}+\mathrm{1}\right)\frac{\left({x}+\mathrm{1}\right)\left({x}−\mathrm{3}\right)^{\mathrm{2}} }{\left({x}−\mathrm{1}\right)^{\mathrm{2}} \left({x}−\mathrm{4}\right)\:}\:{then} \\ $$$${a}.\:{find}\:{x}\:{and}\:{y}\:{intercepts} \\ $$$${b}.\:{find}\:{vertical}\:{asymptote}\:{and}\:{horizontal}\:{asymtote} \\ $$$${c}.\:{find}\:{domain}\:{and}\:{range}\:{of}\:{f} \\ $$$${d}.\:{draw}\:{the}\:{graph}\:{of}\:{f} \\ $$ Answered by Rio…
Question Number 144180 by Willson last updated on 22/Jun/21 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{\mathrm{0}} {\int}^{\:+\infty} \:\frac{\boldsymbol{\mathrm{sh}}\left(\boldsymbol{\alpha\mathrm{t}}\right)}{\boldsymbol{\mathrm{sh}}\left(\boldsymbol{\mathrm{t}}\right)}\boldsymbol{{dt}}\:=\:\frac{\boldsymbol{\pi}}{\mathrm{2}}\boldsymbol{{tan}}\left(\frac{\boldsymbol{\pi\alpha}}{\mathrm{2}}\right) \\ $$ Answered by mindispower last updated on 22/Jun/21 $$=\int_{\mathrm{0}} ^{\infty}…
Question Number 13099 by Joel577 last updated on 14/May/17 $$\mathrm{If}\:{f}\left({x}\:+\:\mathrm{5}\right)\:=\:{g}\left(\mathrm{2}{x}\:−\mathrm{1}\right) \\ $$$$\mathrm{Find}\:\mathrm{2}{f}^{−\mathrm{1}} \left({x}\right) \\ $$$$ \\ $$$$\left(\mathrm{A}\right)\:{g}^{−\mathrm{1}} \left({x}\right)\:+\:\mathrm{11}\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:{g}^{−\mathrm{1}} \left({x}/\mathrm{2}\right)\:+\:\mathrm{6} \\ $$$$\left(\mathrm{B}\right)\:{g}^{−\mathrm{1}} \left({x}\right)\:+\:\mathrm{9}\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{E}\right)\:{g}^{−\mathrm{1}} \left(\mathrm{2}{x}\right)\:+\:\mathrm{6} \\ $$$$\left(\mathrm{C}\right)\:{g}^{−\mathrm{1}}…
Question Number 78622 by mathmax by abdo last updated on 19/Jan/20 $${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\:\:\int_{\mathrm{0}} ^{{n}} \left(\mathrm{1}−\frac{{t}}{{n}}\right)^{{n}} {ln}\left(\mathrm{1}+{nt}\right){dt} \\ $$ Commented by mathmax by abdo last updated…
Question Number 78620 by mathmax by abdo last updated on 19/Jan/20 $${explicit}\:\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{+\infty} {ln}\left(\mathrm{1}−{xe}^{−{t}} \right){dt}\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$ Answered by mind is power last updated on…
Question Number 78623 by mathmax by abdo last updated on 19/Jan/20 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{\sqrt{\mathrm{1}+{x}+{x}^{\mathrm{2}} +….+{x}^{{n}} }\:\:−\mathrm{1}}{{x}^{\frac{{n}}{\mathrm{2}}} } \\ $$ Answered by jagoll last updated on 19/Jan/20…
Question Number 144109 by henderson last updated on 21/Jun/21 $$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{everybody}}\:! \\ $$$$\mathrm{1}.\:\boldsymbol{\mathrm{calculate}}\::\:\boldsymbol{\mathrm{I}}\:=\int_{\frac{\boldsymbol{\pi}}{\mathrm{6}}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{3}}} \boldsymbol{{ln}}\left(\boldsymbol{{tan}}\:\boldsymbol{{x}}\right)\boldsymbol{{dx}}. \\ $$$$\mathrm{2}.\:\boldsymbol{\mathrm{calculate}}\:\::\:\underset{\boldsymbol{{x}}\:\rightarrow\:\boldsymbol{{e}}} {\boldsymbol{{lim}}}\:\frac{\boldsymbol{{x}}\sqrt{\mathrm{1}−\boldsymbol{{ln}}\:\boldsymbol{{x}}}}{\boldsymbol{{x}}−\boldsymbol{{e}}}\:. \\ $$ Commented by bobhans last updated on…
Question Number 391 by 123456 last updated on 25/Jan/15 $${f}\left[{f}\left({x}\right)\right]={f}\left({x}^{\mathrm{2}} \right) \\ $$ Answered by prakash jain last updated on 27/Dec/14 $$\mathrm{The}\:\mathrm{equation}\:\mathrm{above}\:\mathrm{implies} \\ $$$${f}\left({x}\right)={x}^{\mathrm{2}} \\…