Question Number 132007 by abdullahquwatan last updated on 10/Feb/21 Answered by bramlexs22 last updated on 10/Feb/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{2x}+\mathrm{sin}\:\mathrm{3x}\left(\mathrm{cos}\:\mathrm{x}−\mathrm{cos}\:\mathrm{2x}\right)−\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{cos}\:\mathrm{2x}−\mathrm{1}} \\ $$$$=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{cos}\:\mathrm{2x}−\mathrm{cos}\:\mathrm{x}\right)\left(\mathrm{1}−\mathrm{sin}\:\mathrm{3x}\right)}{\mathrm{cos}\:\mathrm{2x}−\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}} \\ $$$$=\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 66468 by mathmax by abdo last updated on 15/Aug/19 $${calculate}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left({x}^{{n}} \:+\mathrm{3}\right)^{\mathrm{2}} }\:\:{with}\:{n}>\mathrm{1} \\ $$ Commented by mathmax by abdo last…
Question Number 933 by 123456 last updated on 29/Apr/15 $${f}\left({x}\right)=\frac{\mathrm{ln}\:{x}}{{x}} \\ $$$$\underset{\mathrm{1}} {\overset{{e}} {\int}}\:\frac{{f}\left({x}\right)}{{x}}{dx}=? \\ $$$$\:\underset{\mathrm{1}} {\overset{{e}} {\int}}\frac{\mathrm{ln}\:{f}\left({x}\right)}{{x}}{dx}=? \\ $$ Commented by prakash jain last…
Question Number 132006 by bramlexs22 last updated on 10/Feb/21 $$\:\mathrm{Given}\:\begin{cases}{\sqrt{\mathrm{2}}\:\mathrm{cos}\:\mathrm{A}=\mathrm{cos}\:\mathrm{B}+\mathrm{cos}\:^{\mathrm{3}} \mathrm{B}}\\{\sqrt{\mathrm{2}}\:\mathrm{sin}\:\mathrm{A}=\mathrm{sin}\:\mathrm{B}−\mathrm{sin}\:^{\mathrm{3}} \mathrm{B}}\end{cases} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}\:\left(\mathrm{A}−\mathrm{B}\right). \\ $$ Answered by EDWIN88 last updated on 10/Feb/21 $$\:\begin{cases}{\mathrm{2cos}\:^{\mathrm{2}} \mathrm{A}=\mathrm{cos}\:^{\mathrm{2}}…
Question Number 66469 by $@ty@m123 last updated on 15/Aug/19 Commented by $@ty@m123 last updated on 15/Aug/19 $${BD}\:{and}\:{CE}\:{are}\:{altitudes}\:{of}\:\bigtriangleup{ABC}. \\ $$$${Prove}\:{that}\:{AG}={AF} \\ $$ Terms of Service Privacy…
Question Number 66466 by mathmax by abdo last updated on 15/Aug/19 $${find}\:\:{f}\left({a},{b}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left({ax}\right){cos}\left({bx}\right)}{\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \right)}{dx}\:\:{with}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left({x}\right){cos}\left(\mathrm{2}{x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{4}\right)}{dx} \\…
Question Number 931 by sai dinesh last updated on 29/Apr/15 $$\mathrm{4}.\mathrm{4}.\mathrm{4}.\mathrm{4}=\mathrm{20}? \\ $$$${in}\:{this}\:{question}\:{the}\:.\:{representss} \\ $$$${any}\:{symbol}\:{find}? \\ $$ Answered by prakash jain last updated on 29/Apr/15…
Question Number 132000 by bramlexs22 last updated on 10/Feb/21 $$\:\mathrm{super}\:\mathrm{nice}\: \\ $$$$\:\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{1}}{\left(\mathrm{x}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\right)^{\mathrm{2}} }\:\right)\mathrm{dx} \\ $$ Answered by EDWIN88 last updated on…
Question Number 66467 by mathmax by abdo last updated on 15/Aug/19 $${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({n}+{x}^{{n}} \right)^{\mathrm{2}} }\:\:\:{with}\:{n}>\mathrm{1} \\ $$ Commented by mathmax by abdo last…
Question Number 66464 by mathmax by abdo last updated on 15/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)\left({x}^{\mathrm{2}} +\mathrm{8}\right)^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last…