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Question Number 195263 Answers: 2 Comments: 0
$$\:\:\:\:\:\:\begin{cases}{{y}\:\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\:=\:\mathrm{2}}\\{\mathrm{4sin}\:{x}−\mathrm{2}{y}\:\mathrm{cos}\:{x}\:=\:{y}}\end{cases} \\ $$$$\:\:\:\:\:\:\:\mathrm{tan}\:{x}\:=?\: \\ $$
Question Number 195259 Answers: 0 Comments: 1
$${prove}\:{that} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{{e}^{{n}} \centerdot\left({n}!\right)}{{n}^{{n}} \:\sqrt{{n}}}=\sqrt{\mathrm{2}\pi} \\ $$
Question Number 195255 Answers: 2 Comments: 0
$$\int\frac{{dx}}{\mathrm{cos}\:^{\mathrm{3}} {x}\sqrt{\mathrm{4sin}\:{x}\mathrm{cos}\:{x}}} \\ $$
Question Number 195254 Answers: 1 Comments: 0
$$\int^{\boldsymbol{{spillover}}} \frac{\mathrm{sin}\:^{\mathrm{2}} {x}\mathrm{cos}\:^{\mathrm{2}} {x}}{\left(\mathrm{sin}\:^{\mathrm{5}} {x}+\mathrm{cos}\:^{\mathrm{3}} {x}\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{sin}\:^{\mathrm{3}} {x}\mathrm{cos}\:^{\mathrm{2}} {x}+\mathrm{cos}\:^{\mathrm{5}} {x}\right)^{\mathrm{2}} }{dx} \\ $$
Question Number 195253 Answers: 2 Comments: 1
$${If}\:\mathrm{10sin}\:^{\mathrm{4}} {x}+\mathrm{15cos}\:^{\mathrm{4}} {x}=\mathrm{6}. \\ $$$${find}\:{the}\:{value}\:{of} \\ $$$$\mathrm{27cosec}\:^{\mathrm{6}} {x}+\mathrm{8sec}\:^{\mathrm{6}} {x} \\ $$$$ \\ $$
Question Number 195252 Answers: 1 Comments: 0
$$\int_{\boldsymbol{{spillover}}} \:\:\:\:\:\:\frac{{dx}}{\:\sqrt{{e}^{\mathrm{5}{x}} }\:\sqrt{\left({e}^{\mathrm{2}{x}} +{e}^{−\mathrm{2}{x}} \right)^{\mathrm{3}} }} \\ $$
Question Number 195251 Answers: 0 Comments: 1
$${If}\:\:{x}^{\left[\mathrm{16}\left(\mathrm{log}\:_{\mathrm{5}} {x}\right)^{\mathrm{3}} −\mathrm{68log}\:_{\mathrm{5}} {x}\right]} =\mathrm{5}^{−\mathrm{16}} \: \\ $$$$\:{then}\:{Find}\:{the}\:{the}\:{product}\:{of}\:{x} \\ $$$$ \\ $$
Question Number 195248 Answers: 0 Comments: 3
Question Number 195232 Answers: 0 Comments: 0
$${a},\:{b},\:{c}>\mathrm{0},\:\:{a}+{b}+{c}\geqslant\mathrm{1}.\:\mathrm{Find} \\ $$$$\mathrm{max}\:\underset{\mathrm{cyc}} {\sum}\:\frac{{a}−{bc}}{{a}+{bc}}. \\ $$
Question Number 195231 Answers: 1 Comments: 0
$$\:\:\:\:\:\begin{array}{|c|}{\:\cancel{\underline{\underbrace{ }}}}\\\hline\end{array} \\ $$
Question Number 195229 Answers: 0 Comments: 9
$${below}\:{equestion}\:{is}\:{show}\:\:{elips}\:{and} \\ $$$${hypharabollah} \\ $$$$\frac{{x}^{\mathrm{2}} }{{cos}\mathrm{3}}+\frac{{y}^{\mathrm{2}} }{{sin}\mathrm{3}}=\mathrm{1} \\ $$
Question Number 195227 Answers: 0 Comments: 0
$$ \\ $$$$\alpha_{\mathrm{1}} ^{\mathrm{3}} \left[\frac{\underset{{i}=\mathrm{2}} {\overset{{n}} {\prod}}\left({x}−\alpha_{{i}} \right)}{\underset{{i}=\mathrm{2}} {\overset{{n}} {\prod}}\left(\alpha_{\mathrm{1}} −\alpha_{{i}} \right)}\right]+\underset{{j}=\mathrm{2}} {\overset{{n}} {\sum}}\left(\alpha_{{j}} ^{\mathrm{3}} \left[\frac{\underset{{i}=\mathrm{1}} {\overset{{j}−\mathrm{1}} {\prod}}\left({x}−\alpha_{{i}} \right)\underset{{i}={j}+\mathrm{1}} {\overset{{n}} {\prod}}\left({x}−\alpha_{{j}} \right)}{\underset{{i}=\mathrm{1}} {\overset{{j}−\mathrm{1}} {\prod}}\left(\alpha_{{j}} −\alpha_{{i}} \right)\underset{{i}={j}+\mathrm{1}} {\overset{{n}} {\prod}}\left(\alpha_{{j}} −\alpha_{{i}} \right)}\right]+\alpha_{{n}} ^{\mathrm{3}} \left[\frac{\underset{{i}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\prod}}\left({x}−\alpha_{{i}} \right)}{\underset{{i}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\prod}}\left(\alpha_{{n}} −\alpha_{{i}} \right)}\right]−{x}^{\mathrm{3}} =\mathrm{0}\right. \\ $$$${solve}\:{for}\:{x}\:.\:\:\:\:\:\:\:\:\:\:\:\:\left[\:{where}\:{n}\geqslant\mathrm{5}\:\right] \\ $$
Question Number 195224 Answers: 2 Comments: 0
$$\:\:\:\:\:\:\:\int_{\mathrm{1}} ^{\mathrm{e}} \mathrm{0}\:{dx}\:=\:?? \\ $$
Question Number 195208 Answers: 4 Comments: 0
Question Number 195202 Answers: 0 Comments: 0
Question Number 195203 Answers: 1 Comments: 0
$$\mathrm{Calculer}\:\underset{\:\mathrm{0}} {\int}^{\:+\infty} \frac{\mathrm{dt}}{\left(\mathrm{e}^{\mathrm{t}} −\mathrm{e}^{−\mathrm{t}} \right)^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} } \\ $$
Question Number 195195 Answers: 1 Comments: 1
$$\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{limit}: \\ $$$$\:\underset{\mathrm{x}\rightarrow\mathrm{a}\:} {\overset{\mathrm{lim}} {\:}}\:\:\:\frac{\boldsymbol{\mathrm{x}}^{\frac{\mathrm{1}}{\mathrm{3}}} }{\boldsymbol{\mathrm{x}}^{\frac{\mathrm{1}}{\mathrm{2}}} }\:−\:\frac{\boldsymbol{\mathrm{a}}^{\frac{\mathrm{1}}{\mathrm{3}}} }{\boldsymbol{\mathrm{a}}^{\frac{\mathrm{1}}{\mathrm{2}}} } \\ $$
Question Number 195194 Answers: 2 Comments: 0
Question Number 195192 Answers: 1 Comments: 0
$$ \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{sinx}+\frac{\pi}{\mathrm{2}}\right)^{\mathrm{x}} =? \\ $$
Question Number 195206 Answers: 1 Comments: 0
Question Number 195185 Answers: 0 Comments: 0
$$\mathrm{1}/\:\:\mathrm{Montrer}\:\mathrm{que}\:\underset{\:\mathrm{0}} {\int}^{\:+\infty} \:\frac{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{2}{p}−\mathrm{1}} }{\mathrm{1}−{x}^{\mathrm{4}{p}} }{dx}=\left(\frac{\mathrm{2}^{\mathrm{2}{p}−\mathrm{3}} }{{p}}\right)\pi\left[\mathrm{1}+\mathrm{2}\underset{{k}=\mathrm{1}} {\overset{{p}−\mathrm{1}} {\sum}}{cos}^{\mathrm{2}{p}−\mathrm{1}} \left(\frac{{k}\pi}{\mathrm{2}{p}}\right)\right] \\ $$$$\mathrm{2}/\:\:\:\:\mathrm{En}\:\mathrm{d}\acute {\mathrm{e}duire}\:\underset{\:\mathrm{0}} {\int}^{\:\mathrm{1}} \frac{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{2}{p}−\mathrm{1}} }{\mathrm{1}−{x}^{\mathrm{4}{p}} }{dx} \\ $$
Question Number 195180 Answers: 1 Comments: 0
$$ \\ $$$$\mathrm{1}.\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{sinx}\:\:\:\:\:\:,\:\:\:\:\frac{\pi}{\mathrm{2}}<\mathrm{x}\leqslant\mathrm{2}\pi}\\{\mathrm{cosx}\:\:\:\:\:\:,\:\:\:\:\:\mathrm{0}\leqslant\mathrm{x}\leqslant\frac{\pi}{\mathrm{2}}}\end{cases} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{f}^{'} \left(\frac{\pi}{\mathrm{2}}\right)\:=? \\ $$$$\mathrm{2}.\:\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{sinx}\:\:\:\:\:\:,\:\:\:\:\frac{\pi}{\mathrm{2}}<\mathrm{x}\leqslant\mathrm{2}\pi}\\{\mathrm{cosx}\:\:\:\:\:\:,\:\:\:\:\:\mathrm{0}\leqslant\mathrm{x}\leqslant\frac{\pi}{\mathrm{2}}}\end{cases} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{f}'\left(\mathrm{2}\pi\right)\:=? \\ $$$$ \\ $$
Question Number 195178 Answers: 2 Comments: 0
Question Number 195175 Answers: 1 Comments: 0
Question Number 195171 Answers: 0 Comments: 0
Question Number 195170 Answers: 2 Comments: 0
$${f}\left({x}\right)=\begin{cases}{{x}^{\mathrm{7}} +\mathrm{2}{x}+\mathrm{1}\:\:\:\:\:\:\:;{x}\geqslant\mathrm{2}}\\{{x}^{\mathrm{2}} +\mathrm{7}{x}+\mathrm{4}\:\:\:\:\:\:\:\:;{x}<\mathrm{1}}\end{cases} \\ $$$${f}^{'} \left(\mathrm{1}\right)=? \\ $$
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