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Question Number 89271 Answers: 0 Comments: 1
$$\frac{\mathrm{3}}{\mathrm{4}}×\frac{\mathrm{8}}{\mathrm{9}}×\frac{\mathrm{15}}{\mathrm{16}}×...×\frac{\mathrm{2499}}{\mathrm{2500}} \\ $$
Question Number 89311 Answers: 0 Comments: 0
$$\:\:{Show}\:{that} \\ $$$$\underset{\:\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\:\mathrm{1}} {\int}}\left\{\underset{\:\:\:\:\mathrm{0}} {\overset{\:\:\:\mathrm{1}} {\int}}\frac{{x}−{y}}{\left({x}+{y}\right)^{\mathrm{2}} }{dy}\right\}{dx}=\underset{\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\:\mathrm{1}} {\int}}\left\{\underset{\:\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\mathrm{1}} {\int}}\frac{{x}−{y}}{\left({x}+{y}\right)^{\mathrm{2}} }{dx}\right\}{dy} \\ $$$$ \\ $$
Question Number 89259 Answers: 0 Comments: 2
$${hello}\: \\ $$$${any}\:{good}\:{books}\:{to}\:{learn}\:{calculas}\:{and} \\ $$$${series}? \\ $$
Question Number 89255 Answers: 0 Comments: 3
$$\mathrm{1}\rangle\underset{{k}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{k}^{{n}} {k}!} \\ $$$$\mathrm{2}\rangle\int_{\mathrm{0}} ^{\infty} \left({xe}^{\mathrm{1}−{x}} −\lfloor{x}\rfloor{e}^{\mathrm{1}−\lfloor{x}\rfloor} \right){dx} \\ $$
Question Number 89244 Answers: 0 Comments: 1
Question Number 89243 Answers: 3 Comments: 0
$${solve}\:{the}\:{following}\:{diffirntial}\:{equation} \\ $$$$\left.\mathrm{1}\right)\left(\mathrm{2}{x}+{y}\right){dx}+\left({x}+{y}\right){dy}=\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\left(\mathrm{3}{x}−{y}\right){dx}−\left({x}−{y}\right){dy}=\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\:\left({cos}\left({x}\right)+{y}\right){dx}\:+\:\left(\mathrm{2}{y}+{x}\right){dy}=\mathrm{0} \\ $$
Question Number 89237 Answers: 0 Comments: 1
$$\int_{\mathrm{2}} ^{\mathrm{1}} \left(\mathrm{x}+\mathrm{1}\right)\left(\sqrt{\left.\mathrm{x}+\mathrm{3}\right)}\right. \\ $$
Question Number 89236 Answers: 1 Comments: 0
$$\mathrm{z}\left(\mathrm{z}^{\mathrm{2}} +\mathrm{3x}\right)+\mathrm{3y}=\mathrm{0} \\ $$$$\mathrm{show}\:\mathrm{that} \\ $$$$\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{x}^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{y}^{\mathrm{2}} }=\frac{\mathrm{2z}\left(\mathrm{x}−\mathrm{1}\right)}{\left(\mathrm{z}^{\mathrm{2}} +\mathrm{x}\right)^{\mathrm{3}} } \\ $$
Question Number 89240 Answers: 0 Comments: 0
$${If}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\pi} {e}^{{x}} {sin}^{{n}} {xdx},\:{show}\:{that}\: \\ $$$$\left({n}^{\mathrm{2}} +\mathrm{1}\right){I}_{{n}} ={n}\left({n}−\mathrm{1}\right){I}_{{n}−\mathrm{2}} \\ $$
Question Number 89238 Answers: 1 Comments: 1
$$\int_{\mathrm{7}} ^{\mathrm{12}} \mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}−\mathrm{3}} \\ $$
Question Number 89226 Answers: 0 Comments: 1
$$\int\left(\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{2}}{\mathrm{x}^{\mathrm{3}} }\right)\sqrt{\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }} \\ $$
Question Number 89239 Answers: 0 Comments: 5
$$\mathrm{A}\:\mathrm{new}\:\mathrm{update}\:\mathrm{has}\:\mathrm{been}\:\mathrm{released}\:\mathrm{to} \\ $$$$\mathrm{fix}\:\mathrm{issues}\:\mathrm{with}\:\mathrm{android}\:\mathrm{10}.\:\mathrm{If}\:\mathrm{you} \\ $$$$\mathrm{have}\:\mathrm{android}\:\mathrm{10}\:\mathrm{phone}\:\mathrm{please}\:\mathrm{download} \\ $$$$\mathrm{latest}\:\mathrm{update}. \\ $$
Question Number 89213 Answers: 1 Comments: 0
$$\int\frac{\sqrt{\mathrm{tan}\:\mathrm{x}\:+\:\mathrm{1}}}{\mathrm{cos}^{\mathrm{2}} \mathrm{x}} \\ $$
Question Number 89228 Answers: 0 Comments: 1
$$\underset{\mathrm{4}} {\overset{\mathrm{5}} {\int}}\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}−\mathrm{4}} \\ $$
Question Number 89205 Answers: 1 Comments: 1
$$\mathrm{2}\:\frac{{dy}}{{dx}}\:=\:\frac{{y}}{{x}}\:+\:\left(\frac{{y}}{{x}}\right)^{\mathrm{2}} \\ $$
Question Number 89202 Answers: 0 Comments: 4
$$\mathrm{sin}\:\left(\frac{\pi}{\mathrm{7}}\right)\mathrm{sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\:=? \\ $$
Question Number 89200 Answers: 0 Comments: 0
Question Number 89194 Answers: 1 Comments: 2
Question Number 89193 Answers: 0 Comments: 3
$$\mathrm{cos}\:{x}−\mathrm{sin}\:{x}\:=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{cos}\:{x}\:\mathrm{sin}\:{x}\:=\:\frac{\mathrm{3}}{\mathrm{8}}\:,\:\pi\:<\:{x}\:<\:\mathrm{2}\pi \\ $$$$\mathrm{cos}\:{x}\:+\:\mathrm{sin}\:{x}\:=? \\ $$
Question Number 89192 Answers: 2 Comments: 2
Question Number 89188 Answers: 2 Comments: 0
$${f}\left({x}\right)\:+\:{f}\left({x}−\mathrm{1}\right)\:\:=\:\:{x}^{\mathrm{2}} \:\:\:,\:\:\:{x}\:\in\:\mathbb{R} \\ $$$${f}\left(\mathrm{19}\right)\:\:=\:\:\mathrm{94} \\ $$$${f}\left(\mathrm{94}\right)\:\:=\:\:...\:\:? \\ $$
Question Number 89187 Answers: 0 Comments: 2
Question Number 89185 Answers: 0 Comments: 1
Question Number 89172 Answers: 1 Comments: 0
Question Number 89153 Answers: 1 Comments: 0
$$\mathrm{If}\:\mathrm{P}=\frac{\mathrm{RE}^{\mathrm{2}} }{\left(\mathrm{R}+\mathrm{B}\right)^{\mathrm{2}} }\:\mathrm{make}\:\mathrm{R}\:\mathrm{the}\:\mathrm{subject}\:\mathrm{of}\:\mathrm{the}\:\mathrm{formula}. \\ $$
Question Number 89146 Answers: 6 Comments: 4
$$\left.\mathrm{1}\right)\int{x}\sqrt{\frac{{x}−\mathrm{2}}{{x}+\mathrm{1}}}\:{dx} \\ $$$$\left.\mathrm{2}\right)\int\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}{dx} \\ $$$$\left.\mathrm{3}\right)\int\sqrt{−{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{10}}\:{dx} \\ $$
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