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Question Number 162787 Answers: 1 Comments: 0
$$\boldsymbol{\mathrm{happy}}\:\boldsymbol{\mathrm{new}}\:\boldsymbol{\mathrm{year}} \\ $$$$\left\{\boldsymbol{{a}};\boldsymbol{{b}};\boldsymbol{{c}}\right\}\in\mathbb{Z}−\left\{\mathrm{0}\right\} \\ $$$$\boldsymbol{{p}}\left(\boldsymbol{{x}}\right)=\boldsymbol{{ax}}^{\mathrm{2}} +\boldsymbol{{bx}}+\boldsymbol{{c}}\:\:\:\: \\ $$$$\boldsymbol{{p}}\left(\boldsymbol{{a}}\right)=\mathrm{0} \\ $$$$\boldsymbol{{p}}\left(\boldsymbol{{b}}\right)=\mathrm{0} \\ $$$$\boldsymbol{{p}}\left(\mathrm{1}\right)=? \\ $$
Question Number 162783 Answers: 0 Comments: 0
Question Number 162782 Answers: 0 Comments: 0
Question Number 162776 Answers: 3 Comments: 0
$$\:\:\:\frac{\mathrm{sin}\:{x}}{\mathrm{1}−\mathrm{cos}\:{x}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\: \\ $$$$\:{x}=? \\ $$
Question Number 162775 Answers: 2 Comments: 0
$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{a}\:\mathrm{sin}\:\mathrm{3}{x}\:−\:{b}\:\mathrm{sin}\:\mathrm{2}{x}\:}{{x}^{\mathrm{3}} }\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:{Find}\:{a}\:{and}\:{b}\:. \\ $$
Question Number 162785 Answers: 1 Comments: 0
Question Number 162747 Answers: 1 Comments: 0
Question Number 162744 Answers: 0 Comments: 0
Question Number 162734 Answers: 1 Comments: 0
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{Happy}\:{New}\:{Year} \\ $$$$\left[\left(\mathrm{10}+\mathrm{9}\right)×\mathrm{8}×\left(\mathrm{7}+\mathrm{6}\right)+\left(\mathrm{5}+\mathrm{4}\right)×\left(\mathrm{3}+\mathrm{2}\right)+\mathrm{1}\right] \\ $$
Question Number 163110 Answers: 1 Comments: 0
Question Number 162728 Answers: 2 Comments: 2
Question Number 162726 Answers: 1 Comments: 0
$$\left.\mathrm{1}\right)\:{Calculate} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{tgx}^{{m}} }{\left(\mathrm{sin}\:{x}\right)^{{n}} },\:\:\left({m},\:{n}\in\: {N}\right) \\ $$$$\left.\mathrm{2}\right)\:{f}'\left({a}\right)\:{e}\mathrm{xiste},\:{calculate} \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}{x}\left[{f}\left({a}+\frac{{a}}{{x}}\right)−{f}\left({a}−\frac{\beta}{{x}}\right)\right],\: \\ $$$$\left(\alpha,\:\beta\:\in\: {R}\right) \\ $$
Question Number 162718 Answers: 0 Comments: 0
$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\int_{\epsilon} ^{\mathrm{1}} \left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} \mathrm{dx}}{\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} \mathrm{dx}}=?\:\:\:\:\:\:\:\left(\mathrm{0}<\epsilon<\mathrm{1}\right) \\ $$
Question Number 162702 Answers: 0 Comments: 0
$$\int\boldsymbol{{e}}^{−\mathrm{4}\boldsymbol{{x}}} \boldsymbol{{tg}}\left(\boldsymbol{{x}}\right)\boldsymbol{{ln}}\mid\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)\mid\boldsymbol{{dx}}=? \\ $$
Question Number 162701 Answers: 1 Comments: 0
Question Number 164806 Answers: 1 Comments: 7
Question Number 162721 Answers: 3 Comments: 0
$$ \\ $$$$\:\:\:\:\:\:\:{calculate}\: \\ $$$$\:\:\:\:\:\:{f}\:\left({x}\:\right)=\:\frac{\:\mathrm{1}}{\mathrm{4}\left(\mathrm{1}+{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)\right)\:}\:+\frac{\mathrm{1}}{\mathrm{9}\left(\mathrm{1}−{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)\right)}\:\:\left(\:{x}\:\neq\:\mathrm{2}{k}\:\pi\:,\:{k}\:\in\:\mathbb{Z}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{f}_{\:{min}} =\:? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathscr{A}{dapted}\:\mathscr{F}{rom}\:\mathscr{I}{nstagram}\: \\ $$$$ \\ $$
Question Number 163178 Answers: 1 Comments: 0
Question Number 162715 Answers: 2 Comments: 0
$$\:\:\:\mid\mid{x}−\mathrm{1}\mid−\mathrm{5}\mid\:\geqslant\:\mathrm{2}\:\:{has}\:{solution}\:{set} \\ $$$$\:{is}\:{a}\:\leqslant{x}\leqslant{b}\:{or}\:{x}\leqslant\:{c}\:\cup\:{x}\geqslant{d}\:. \\ $$$$\:{Find}\:\frac{{a}+{d}}{{b}+{c}}\:. \\ $$
Question Number 162675 Answers: 1 Comments: 0
$${y}\:=\:\sqrt{{x}} \\ $$$${Find}\:\:\:\frac{{dy}}{{dx}}\:\:{by}\:{first}\:{principle}. \\ $$
Question Number 162674 Answers: 2 Comments: 0
Question Number 162673 Answers: 1 Comments: 0
Question Number 162672 Answers: 2 Comments: 0
$${Calculate} \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left(\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} }−\sqrt{{x}^{\mathrm{2}} −\mathrm{2}{x}}\right) \\ $$$$\underset{{x}\rightarrow\mathrm{7}} {\mathrm{lim}}\frac{\sqrt{{x}+\mathrm{2}}−\sqrt[{\mathrm{3}}]{{x}+\mathrm{20}}}{\:\sqrt[{\mathrm{4}}]{{x}+\mathrm{9}}−\mathrm{2}} \\ $$
Question Number 162651 Answers: 1 Comments: 0
Question Number 162649 Answers: 3 Comments: 0
$$\:\mathrm{sin}\:^{\mathrm{10}} \left({x}\right)+\mathrm{cos}\:^{\mathrm{10}} \left({x}\right)=\frac{\mathrm{11}}{\mathrm{36}} \\ $$$$\:\mathrm{sin}\:^{\mathrm{12}} \left({x}\right)+\mathrm{cos}\:^{\mathrm{12}} \left({x}\right)=? \\ $$
Question Number 162643 Answers: 3 Comments: 0
$$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{4}/\mathrm{3}} \:\left(\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} +\mathrm{1}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{3}−{x}^{\mathrm{2}} }\:\right)\:=? \\ $$
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