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
Question Number 166612 by mnjuly1970 last updated on 23/Feb/22 $$ \\ $$$$\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{1}}{\mathrm{1}+{cos}\left({x}\right)+\mathrm{2}{sin}\left({x}\right)}{dx}=? \\ $$ Commented by cortano1 last updated on 23/Feb/22 $$\:\mathrm{1}+\mathrm{cos}\:\mathrm{x}+\mathrm{2sin}\:\mathrm{x}=\:\mathrm{cos}\:^{\mathrm{2}} \frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}+\mathrm{sin}\:^{\mathrm{2}}…
Question Number 101075 by bemath last updated on 30/Jun/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{arcsin}\:\left(\mathrm{x}^{\mathrm{2}} \right)−\mathrm{x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{4}} \:\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}\:=\:? \\ $$ Commented by Dwaipayan Shikari last updated on 30/Jun/20…
Question Number 166606 by mathlove last updated on 23/Feb/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 166584 by amin96 last updated on 22/Feb/22 Commented by bobhans last updated on 22/Feb/22 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{a}\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} \Rightarrow\mathrm{12}=\mathrm{a}\left(\mathrm{4}\right);\:\mathrm{a}=\mathrm{3} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3}\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} \Rightarrow\mathrm{f}\left(\mathrm{10}\right)=\mathrm{3}×\mathrm{64}=\mathrm{192} \\ $$ Answered by…
Question Number 166572 by qaz last updated on 22/Feb/22 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{2n}} {\sum}}\mathrm{2}^{−\mathrm{k}} \mathrm{cos}\:\sqrt{\frac{\mathrm{k}}{\mathrm{n}}}=? \\ $$ Answered by alephzero last updated on 23/Feb/22 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{0}}…