Question Number 128145 by mnjuly1970 last updated on 04/Jan/21 Commented by mnjuly1970 last updated on 04/Jan/21 $${number}\:{of}\:{triangles}…\uparrow\uparrow \\ $$ Commented by mr W last updated…
Question Number 128135 by help last updated on 04/Jan/21 Commented by liberty last updated on 04/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{3sin}\:\mathrm{5x}}{\mathrm{x}}\right)^{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{4x}}{\mathrm{x}^{\mathrm{2}} }\right)} =\:\mathrm{15}^{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}−\left(\mathrm{1}−\frac{\mathrm{16x}^{\mathrm{2}} }{\mathrm{2}}\right)}{\mathrm{x}^{\mathrm{2}} }\right)} \\…
Question Number 128132 by I want to learn more last updated on 04/Jan/21 $$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{x}}\right)\:\:\:=\:\:\:\mathrm{x}^{\mathrm{4}} \:\:+\:\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} }\:,\:\:\:\:\:\mathrm{find}\:\:\mathrm{f}\left(\mathrm{5}\right) \\ $$ Answered by Olaf last updated on 04/Jan/21…
Question Number 62596 by aliesam last updated on 23/Jun/19 $$\int\mathrm{sin}^{\mathrm{100}} \left(\mathrm{x}\right)\:\mathrm{cos}^{\mathrm{100}} \left(\mathrm{x}\right)\:\mathrm{dx} \\ $$ Answered by MJS last updated on 23/Jun/19 $$\int\mathrm{sin}^{\mathrm{100}} \:{x}\:\mathrm{cos}^{\mathrm{100}} \:{x}\:{dx}=\int\left(\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}\right)^{\mathrm{100}} {dx}=…
Question Number 128130 by physicstutes last updated on 04/Jan/21 $$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\:\mathrm{sin}\left(\mathrm{2}{x}\:+\:\mathrm{2}{h}\right)−\mathrm{sin}\:\mathrm{2}{x}\:=\:\mathrm{2cos}\left(\mathrm{2}{x}\:+{h}\right)\mathrm{sin}\:{h} \\ $$ Answered by Olaf last updated on 04/Jan/21 $$\mathrm{sin}{a}−\mathrm{sin}{b}\:=\:\mathrm{2sin}\left(\frac{{a}−{b}}{\mathrm{2}}\right)\mathrm{cos}\left(\frac{{a}+{b}}{\mathrm{2}}\right)\:\left(\mathrm{1}\right) \\ $$$${a}\:=\:\mathrm{2}{x}+\mathrm{2}{h}\:\mathrm{and}\:{b}\:=\:\mathrm{2}{x} \\…
Question Number 62595 by Pranay last updated on 23/Jun/19 $${what}\:{is}\:\mathrm{2}{sin}^{\mathrm{2}} \theta{cos}^{\mathrm{2}} \theta\:? \\ $$ Commented by ajfour last updated on 23/Jun/19 $${same}\:{as}\:\:\mathrm{2}×\frac{{p}^{\mathrm{2}} }{{h}^{\mathrm{2}} }×\frac{{b}^{\mathrm{2}} }{{h}^{\mathrm{2}}…
Question Number 128126 by Agnibhoo last updated on 04/Jan/21 $$\:\frac{\mathrm{4}}{\mathrm{99}}\:+\:\frac{\mathrm{7}}{\mathrm{999}}\:+\:\frac{\mathrm{11}}{\mathrm{999999}}\:=\:? \\ $$ Answered by Geovanek last updated on 04/Jan/21 $$\frac{\mathrm{4}}{\mathrm{99}}\:+\:\frac{\mathrm{7}}{\mathrm{99}}\:+\:\frac{\mathrm{11}}{\mathrm{999999}}\:=\:{X} \\ $$$$\mathrm{We}\:\mathrm{can}\:\mathrm{see}\:\mathrm{that} \\ $$$$\frac{\mathrm{999999}}{\mathrm{99}}\:=\:\mathrm{10101}\:\:\:\boldsymbol{\mathrm{AND}} \\…
Question Number 128124 by shaker last updated on 04/Jan/21 Answered by Dwaipayan Shikari last updated on 04/Jan/21 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\sqrt[{{n}}]{\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)\left(\mathrm{1}+\frac{\mathrm{2}}{{n}}\right)…\left(\mathrm{1}+\frac{{n}}{{n}}\right)}={y} \\ $$$$\Rightarrow\frac{\mathrm{1}}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{log}\left(\mathrm{1}+\frac{{k}}{{n}}\right)={logy} \\ $$$$\Rightarrow\int_{\mathrm{0}}…
Question Number 128122 by Dwaipayan Shikari last updated on 04/Jan/21 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{16}}+\frac{\mathrm{5}^{\mathrm{2}} }{\mathrm{16}^{\mathrm{2}} .\mathrm{2}!}+\frac{\mathrm{5}^{\mathrm{2}} .\mathrm{9}^{\mathrm{2}} }{\mathrm{16}^{\mathrm{3}} .\mathrm{3}!}+\frac{\mathrm{5}^{\mathrm{2}} .\mathrm{9}^{\mathrm{2}} .\mathrm{13}^{\mathrm{2}} }{\mathrm{16}^{\mathrm{4}} .\mathrm{4}!}+…=\frac{\sqrt{\pi}}{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\right)}={F}_{\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{4}},\frac{\mathrm{1}}{\mathrm{4}},\mathrm{1};\mathrm{1}\right) \\ $$$${Prove}\:{The}\:{above}\:{relation} \\…
Question Number 62587 by Jmasanja last updated on 23/Jun/19 $${three}\:{forces}\:{having}\:{equal}\:{magnitude} \\ $$$${s}\:{of}\:\mathrm{10}{N},\mathrm{20}{N}\:{and}\:\mathrm{30}{N}\:{make}\:{angles}\: \\ $$$${of}\:\mathrm{30}°,\mathrm{120}°\:{and}\:\mathrm{210}°\:{respectively}\:{with} \\ $$$${the}\:{positive}\:{direction}\:{of}\:{the}\:{x}\:{axis}. \\ $$$${By}\:{scale}\:{drawing}\:{find}\:{the}\:{magnitude} \\ $$$${and}\:{the}\:{direction}\:{of}\:{the}\:{resultant}\: \\ $$$${force} \\ $$ Commented…