Question Number 35726 by abdo mathsup 649 cc last updated on 22/May/18 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{\mathrm{1}−{cos}\left({sinx}\right)}{{x}^{\mathrm{2}} } \\ $$ Commented by abdo mathsup 649 cc last updated…
Question Number 35715 by math1967 last updated on 22/May/18 $${Find}\underset{{n}\rightarrow\infty} {\:{lim}}\frac{\mathrm{3}^{{n}+\mathrm{1}} +\mathrm{2}^{{n}+\mathrm{1}} }{\mathrm{3}^{{n}} +\mathrm{2}^{{n}} } \\ $$ Commented by abdo mathsup 649 cc last updated…
Question Number 101239 by M±th+et+s last updated on 01/Jul/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+……+\frac{\mathrm{1}}{{n}}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{5}}……+\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}}}\right) \\ $$ Answered by mathmax by abdo last updated on 01/Jul/20 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+….+\frac{\mathrm{1}}{\mathrm{n}}\:=\mathrm{H}_{\mathrm{n}} \\ $$$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{5}}+….+\frac{\mathrm{1}}{\mathrm{2n}+\mathrm{1}}\:=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…..+\frac{\mathrm{1}}{\mathrm{2n}}+\frac{\mathrm{1}}{\mathrm{2n}+\mathrm{1}}\:−\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{4}}−…−\frac{\mathrm{1}}{\mathrm{2n}}…
Question Number 166771 by cortano1 last updated on 27/Feb/22 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}−\mathrm{cos}\:\mathrm{x}}−\sqrt[{\mathrm{3}}]{\mathrm{sin}\:\mathrm{x}}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}\:=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 166735 by qaz last updated on 26/Feb/22 $$\mathrm{For}\:\:\mathrm{some}\:\mathrm{constant}\:\alpha\in\left(\mathrm{0},\mathrm{1}\right) \\ $$$$\mathrm{calculate}:\:\:\:\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\frac{\mathrm{t}^{\alpha} }{\alpha}−\mathrm{xt}} \mathrm{dt}\sim\sqrt{\frac{\mathrm{2}\pi}{\mathrm{1}−\alpha}}\centerdot\mathrm{x}^{−\frac{\alpha}{\mathrm{2}\left(\mathrm{1}−\alpha\right)}−\mathrm{1}} \mathrm{e}^{\frac{\mathrm{1}−\alpha}{\alpha}\centerdot\mathrm{x}^{−\frac{\alpha}{\mathrm{1}−\alpha}} } ,\mathrm{x}\rightarrow\mathrm{0}^{+} \\ $$ Terms of Service Privacy…
Question Number 166699 by qaz last updated on 25/Feb/22 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{n}} {\overset{\mathrm{2n}} {\sum}}\mathrm{sin}\:\frac{\pi}{\mathrm{k}}=? \\ $$ Answered by mathsmine last updated on 25/Feb/22 $$\:{x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}\leqslant{sin}\left({x}\right)\leqslant{x}……{E} \\…
Question Number 101148 by john santu last updated on 30/Jun/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\left(\mathrm{ln}\:\left(\mathrm{1}+\mathrm{x}\right)\right)−\mathrm{ln}\left(\mathrm{1}+\mathrm{sin}\:\mathrm{x}\right)}{\mathrm{sin}\:^{\mathrm{4}} \left(\frac{\mathrm{x}}{\mathrm{2}}\right)}\:=?\: \\ $$ Commented by bramlex last updated on 01/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\frac{\mathrm{cos}\:\left(\mathrm{ln}\left(\mathrm{1}+{x}\right)\right)}{\mathrm{1}+{x}}\:−\:\frac{\mathrm{cos}\:{x}}{\mathrm{1}+\mathrm{sin}\:{x}}}{\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{4sin}\:^{\mathrm{3}} \left(\frac{{x}}{\mathrm{2}}\right)×\mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)}…
Question Number 166648 by alcohol last updated on 24/Feb/22 $${u}_{{n}+\mathrm{1}} \:=\:\sqrt{\mathrm{2}+{u}_{{n}} } \\ $$$${show}\:{that}\:{u}_{{n}+\mathrm{1}} −{u}_{{n}} \:{and}\:{u}_{{n}} −{u}_{{n}−\mathrm{1}} \\ $$$${have}\:{same}\:{sign} \\ $$$$ \\ $$ Answered by…
Question Number 166627 by cortano1 last updated on 23/Feb/22 $$\:\:\:\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}+\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{5}} +…+\mathrm{x}^{\mathrm{n}} \:\mathrm{and}\: \\ $$$$\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{f}^{\mathrm{2}} \left(\mathrm{x}\right)−\mathrm{f}^{\mathrm{2}} \left(\mathrm{1}\right)}{\mathrm{x}−\mathrm{1}}\:=\:\mathrm{2}^{\mathrm{10}} \:\mathrm{then}\:\mathrm{n}\:=\:? \\ $$ Commented by MJS_new last…
Question Number 166616 by qaz last updated on 23/Feb/22 $$\mathrm{calculate}::\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mid\mathrm{cos}\:\mathrm{1}^{\mathrm{2}} \mid+\mathrm{cos}\:\mid\mathrm{2}^{\mathrm{2}} \mid+\mid\mathrm{cos}\:\mathrm{3}^{\mathrm{2}} \mid+…+\mid\mathrm{cos}\:\mathrm{n}^{\mathrm{2}} \mid}{\mathrm{n}}=\frac{\mathrm{2}}{\pi} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com