Question Number 135786 by JulioCesar last updated on 16/Mar/21 Commented by Ar Brandon last updated on 16/Mar/21 $$\mathrm{You}\:\mathrm{mean}\: \\ $$$$\mathrm{H}=\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{n}} }}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{9}}+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{n}} }}\:??? \\ $$…
Question Number 4712 by paonky last updated on 28/Feb/16 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\mathrm{1}−\mathrm{sin}{x}} −{e}^{\mathrm{1}−\mathrm{tan}{x}} }{\mathrm{tan}{x}−\mathrm{sin}{x}}=? \\ $$ Answered by Yozzii last updated on 28/Feb/16 $${Let}\:{l}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\mathrm{1}−{sinx}} −{e}^{\mathrm{1}−{tanx}}…
Question Number 135780 by bramlexs22 last updated on 15/Mar/21 $${If}\:{g}\left(\mathrm{0}\right)=\mathrm{2}\:,\:{g}\:'\left(\mathrm{0}\right)=\mathrm{1}\:{and}\: \\ $$$${f}\left({x}\right)\:=\:{e}^{\mathrm{2}{x}} {g}\left({x}\right).\:{What}\:{the}\:{value} \\ $$$${of}\:{f}^{−\mathrm{1}} \left(\mathrm{2}\right). \\ $$ Commented by bramlexs22 last updated on 16/Mar/21…
Question Number 135777 by mathmax by abdo last updated on 15/Mar/21 $$\mathrm{let}\:\mathrm{U}_{\mathrm{n}} =\int_{−\infty} ^{+\infty} \:\frac{\mathrm{cos}\left(\mathrm{nx}\right)}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx}\:\mathrm{calculate}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \mathrm{e}^{\mathrm{n}^{\mathrm{2}} } \mathrm{U}_{\mathrm{n}} \\ $$ Answered by mathmax…
Question Number 4707 by 314159 last updated on 28/Feb/16 $${Given}\:{that}\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{px}−\mathrm{2}{q}\:{and}\:{x}^{\mathrm{2}} +{q}\:{have}\:{a} \\ $$$${common}\:{factor}\:{x}−{a}\:,\:{where}\:{p},{q}\:{and}\:{a}\:{are}\:{none}\: \\ $$$${zero}\:{constants}\:,\:{show}\:{that}\:\mathrm{9}{p}^{\mathrm{2}} +\mathrm{16}{q}=\mathrm{0}. \\ $$ Commented by prakash jain last updated…
Question Number 135779 by mathmax by abdo last updated on 15/Mar/21 $$\mathrm{calculate}\:\int_{−\infty} ^{\infty} \:\:\:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{4}} −\mathrm{x}+\mathrm{1}\right)} \\ $$ Commented by mathmax by abdo last…
Question Number 135778 by mathmax by abdo last updated on 15/Mar/21 $$\mathrm{find}\:\:\mathrm{u}_{\mathrm{n}} \left(\mathrm{x}\right)\mathrm{if}\:\:\mathrm{u}_{\mathrm{n}} \left(\mathrm{x}\right)+\mathrm{u}_{\mathrm{n}+\mathrm{1}} \left(\mathrm{x}\right)=\frac{\mathrm{x}^{\mathrm{n}} }{\mathrm{n}!} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 4704 by lakshaysethi039 last updated on 25/Feb/16 $${If}\:{a}_{\mathrm{1}} ,{a}_{\mathrm{2}} ,………{a}_{{n}} {be}\:{an}\:{arithmetic}\:{progression}, \\ $$$${then}\:{show}\:{that} \\ $$$$\frac{\mathrm{1}}{{a}_{\mathrm{1}} {a}_{{n}} }\:+\:\frac{\mathrm{1}}{{a}_{\mathrm{2}} {a}_{{n}−\mathrm{1}} }\:+\:\frac{\mathrm{1}}{{a}_{\mathrm{3}} {a}_{{n}−\mathrm{2}} }\:+………….+\frac{\mathrm{1}}{{a}_{{n}} {a}_{\mathrm{1}} }\:…
Question Number 4702 by 314159 last updated on 22/Feb/16 $$\mathrm{Let}\:\mathrm{f}\:\mathrm{and}\:\mathrm{g}\:\mathrm{be}\:\mathrm{functions}\:\mathrm{such}\:\mathrm{that}\:\mathrm{for}\:\mathrm{all} \\ $$$$\mathrm{real}\:\mathrm{number}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y},\mathrm{g}\left(\mathrm{f}\left(\mathrm{x}+\mathrm{y}\right)\right)=\mathrm{f}\left(\mathrm{x}\right)+\left(\mathrm{x}+\mathrm{y}\right)\mathrm{g}\left(\mathrm{y}\right). \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{g}\left(\mathrm{0}\right)+\mathrm{g}\left(\mathrm{1}\right)+\mathrm{g}\left(\mathrm{2}\right)+\mathrm{g}\left(\mathrm{3}\right)+…+\mathrm{g}\left(\mathrm{2016}\right). \\ $$ Commented by prakash jain last updated on 22/Feb/16 $$\mathrm{Let}\:\mathrm{us}\:\mathrm{try}\:\mathrm{for}\:\mathrm{trivial}\:\mathrm{solution}…
Question Number 70237 by mathmax by abdo last updated on 02/Oct/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{xsin}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{4}} }{dx}\:{with}\:\alpha\:{real} \\ $$ Commented by mind is power last updated on…