Question Number 57405 by Abdo msup. last updated on 03/Apr/19 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{\mathrm{1}−{cosx}.{cos}\left(\mathrm{2}{x}\right)….{cos}\left({nx}\right)}{{x}^{\mathrm{2}} } \\ $$$${with}\:{n}\:{integr}\:{natural}\:{not}\:\mathrm{0}. \\ $$ Answered by Smail last updated on 05/Apr/19 $${cosx}=\mathrm{1}−\frac{{x}^{\mathrm{2}}…
Question Number 122917 by Dwaipayan Shikari last updated on 20/Nov/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{tan}^{−\mathrm{1}} {n}}{{n}^{\mathrm{2}} +\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 57348 by rajesh4661kumar@gamil.com last updated on 03/Apr/19 Commented by rajesh4661kumar@gamil.com last updated on 03/Apr/19 $${bunch}\:{of}\:{thanks} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on…
Question Number 122862 by Dwaipayan Shikari last updated on 20/Nov/20 $$\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{7}} }{\left(\mathrm{1}+{x}\right)^{\mathrm{10}} }{dx} \\ $$ Answered by MJS_new last updated on 20/Nov/20 $$=\underset{\mathrm{0}}…
Question Number 57309 by Tawa1 last updated on 02/Apr/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 57284 by Jmasanja last updated on 01/Apr/19 $${y}\:{is}\:{varies}\:{directly}\:{as}\:{the}\:{square}\:{of}\:{x}\:{and} \\ $$$${inversely}\:{as}\:{z}. \\ $$$${if}\:{x}\:{is}\:{inceased}\:{by}\:\mathrm{10\%}\:{and}\:{z}\:\:{is}\: \\ $$$${decreased}\:{by}\:\mathrm{20\%},\:{find}\:{the}\:{percentage} \\ $$$${change}\:{in}\:{y}. \\ $$ Commented by mr W last…
Question Number 188351 by TUN last updated on 28/Feb/23 $$\sqrt{{x}}+\sqrt{\mathrm{3}{x}−\mathrm{2}}={x}^{\mathrm{2}} +\mathrm{1} \\ $$ Answered by MJS_new last updated on 28/Feb/23 $$\mathrm{it}'\mathrm{s}\:\mathrm{obvious}\:\mathrm{that}\:{x}=\mathrm{1} \\ $$ Commented by…
Question Number 122740 by Dwaipayan Shikari last updated on 19/Nov/20 $${Prove}\:{that} \\ $$$${tanx}=\frac{\mathrm{2}}{\pi−\mathrm{2}{x}}−\frac{\mathrm{2}}{\pi+\mathrm{2}{x}}+\frac{\mathrm{2}}{\mathrm{3}{x}−\mathrm{2}\pi}−\frac{\mathrm{2}}{\mathrm{3}{x}+\mathrm{2}\pi}+\frac{\mathrm{2}}{\mathrm{5}{x}−\mathrm{2}\pi}−\frac{\mathrm{2}}{\mathrm{5}{x}+\mathrm{2}\pi}+…. \\ $$ Commented by Dwaipayan Shikari last updated on 19/Nov/20 $${sinx}\:\:{has}\:{value}\:\mathrm{0}\:{at}\:\mathrm{0},\pi,−\pi,\:\mathrm{2}\pi,−\mathrm{2}\pi,…. \\…
Question Number 57184 by Tawa1 last updated on 31/Mar/19 Commented by Tawa1 last updated on 31/Mar/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{shaded}\:\mathrm{portion} \\ $$ Answered by mr W last updated…
Question Number 188218 by pascal889 last updated on 26/Feb/23 Answered by cortano12 last updated on 27/Feb/23 $$\:\mathrm{let}\:\mathrm{log}\:_{\mathrm{x}} \mathrm{10}=\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{10}} \mathrm{x}}\:=\mathrm{p}\:,\:\mathrm{x}>\mathrm{0}\:,\mathrm{x}\neq\mathrm{1} \\ $$$$\Rightarrow\mathrm{2}.\mathrm{log}\:_{\mathrm{x}} \mathrm{10}−\frac{\mathrm{1}}{\mathrm{2}}\left[\mathrm{log}\:_{\mathrm{x}} \left(\frac{\sqrt{\mathrm{x}}}{\mathrm{100}}\right)\right]−\frac{\left(\frac{\mathrm{1}}{\mathrm{2}}\right)}{\mathrm{1}−\mathrm{log}\:_{\mathrm{x}} \mathrm{10}}=−\frac{\mathrm{7}}{\mathrm{2}} \\…