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Question Number 184859 Answers: 2 Comments: 0
$$ \\ $$$$\:\mathrm{Lim}_{\:{x}\rightarrow\infty} \:{x}^{\:\mathrm{4}} \:\left(\:\mathrm{1}−\:{cos}\:\left(\mathrm{1}−\:{cos}\left(\frac{\mathrm{2}}{{x}}\right)\right)\right)=? \\ $$$$ \\ $$
Question Number 184858 Answers: 1 Comments: 0
$$\underset{{n}={o}} {\overset{+{oo}} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}} \\ $$
Question Number 184856 Answers: 0 Comments: 0
$$ \\ $$$$\:\:\:\:\:{f}\left({x}\right)=\:\sqrt{\:\mid\:\underset{} {\overset{} {{x}}}\:\:\mid\:−\mid\:\:{x}\underset{} {\overset{} {−}}\lfloor{ax}\rfloor\:\mid} \\ $$$$\:\:\:\:\:\:;\:\:\:{a}\:\in\:\left[\:\mathrm{3}\:,\:\mathrm{4}\:\right) \\ $$$$\:\:\:\:\:{find}\::\:\:\:\begin{cases}{\:\:{D}_{\:{f}} \:=?\:\left({domain}\:\right)}\\{\:\:\mathcal{R}_{\:{f}} \:=?\:\left({range}\:\right)}\end{cases} \\ $$$$ \\ $$
Question Number 184845 Answers: 0 Comments: 0
$$\mathrm{x}\:\in\:\left[−\mathrm{0},\mathrm{5}\:;\:\mathrm{0},\mathrm{5}\right] \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{all}\:\:\boldsymbol{\mathrm{x}}'\mathrm{s} \\ $$$$\mathrm{1}.\:\mathrm{4sin}^{\mathrm{2}} \pi\mathrm{x}−\mathrm{4sin}\pi\mathrm{x}\:+\:\mathrm{2}\:=\:\mathrm{2sin}^{\mathrm{2}} \pi\mathrm{y}−\mathrm{1} \\ $$$$\mathrm{2}.\:\mathrm{4sin}\pi\mathrm{x}\:=\:\mathrm{4sin}\pi\mathrm{y}\:−\:\mathrm{7}\:−\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \pi\mathrm{x}} \\ $$
Question Number 184843 Answers: 0 Comments: 0
Question Number 184841 Answers: 1 Comments: 0
Question Number 184839 Answers: 3 Comments: 0
$${xy}\:−\:\mathrm{3}{x}\:=\:\mathrm{27}\:−\mathrm{5}{y} \\ $$$${find}\:{all}\:\left({x}\:,\:{y}\right)\:{in}\:\mathbb{Z}^{\mathrm{2}} \\ $$
Question Number 184832 Answers: 4 Comments: 1
$$\mathrm{Given}\:\mathrm{the}\:\mathrm{acceleration}\: \\ $$$$\mathrm{a}=−\mathrm{4sin2t},\:\mathrm{initial}\:\mathrm{velocity}\: \\ $$$$\mathrm{v}\left(\mathrm{0}\right)=\mathrm{2},\:\mathrm{and}\:\mathrm{the}\:\mathrm{initial}\:\mathrm{position}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{body}\:\mathrm{as}\:\mathrm{s}\left(\mathrm{0}\right)=−\mathrm{3},\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{body}'\mathrm{s}\:\mathrm{position}\:\mathrm{at}\:\mathrm{time}\:\mathrm{t}. \\ $$$$ \\ $$$$\mathrm{Hi} \\ $$
Question Number 184828 Answers: 0 Comments: 1
$${Find}\:{x}\:{in}\:{terms}\:{of}\:\:\:{c}\:\:\forall\:\mathrm{0}<{c}<\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$$$\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{36}{x}−\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:=\left\{\mathrm{4}\left({x}^{\mathrm{3}} −{x}−{c}\right)+\mathrm{9}\left(\mathrm{7}{x}^{\mathrm{2}} +\mathrm{1}\right)\right\}^{\mathrm{2}} \\ $$
Question Number 184823 Answers: 1 Comments: 0
$$ \\ $$$$\:\:\:\mathrm{Lim}_{\:{x}\rightarrow\:\mathrm{0}^{\:+} } \:\:\frac{\:\:\mathrm{1}−\:\:\mathrm{cos}\:\left(\:\mathrm{1}−\:\mathrm{cos}\left(\sqrt{{x}}\:\right)\right)}{{x}^{\:\mathrm{4}} } \\ $$
Question Number 184822 Answers: 1 Comments: 0
Question Number 184819 Answers: 2 Comments: 0
$$\:\:{For}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:,\:{maximum}\:{value} \\ $$$$\:\:{of}\:{f}\left({x}\right)={x}\sqrt{\mathrm{1}−{x}+\sqrt{\mathrm{1}−{x}}}\:{is}\:\_\_ \\ $$
Question Number 184798 Answers: 0 Comments: 1
$${Show}\:{that}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}}{\mid{x}\mid}\:\:{does}\:{not}\:{exist} \\ $$
Question Number 184797 Answers: 0 Comments: 1
$${Show}\:{that}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\frac{\mathrm{1}}{{x}}} −\mathrm{1}}{{e}^{\frac{\mathrm{1}}{{x}}} +\mathrm{1}}\:\:\:{does}\:{not}\:{exist} \\ $$
Question Number 184796 Answers: 1 Comments: 2
$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{6}}} {\mathrm{lim}}\frac{\sqrt{\mathrm{3}}\mathrm{sin}\:{x}−\mathrm{cos}\:{x}}{{x}−\frac{\pi}{\mathrm{6}}} \\ $$
Question Number 184795 Answers: 1 Comments: 1
$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:{x}\sqrt{\mathrm{cos}\:\mathrm{2}{x}}\:}{{x}^{\mathrm{2}} } \\ $$
Question Number 184794 Answers: 4 Comments: 2
$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{5}} −\mathrm{32}}{{x}^{\mathrm{3}} −\mathrm{8}} \\ $$
Question Number 184793 Answers: 1 Comments: 0
$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\:\frac{{x}^{\mathrm{2}} −\mathrm{4}}{\:\sqrt{\mathrm{3}{x}−\mathrm{2}}−\sqrt{{x}+\mathrm{2}}} \\ $$$$ \\ $$
Question Number 184792 Answers: 1 Comments: 2
$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:{x}−\mathrm{sin}\:{x}}{\mathrm{sin}\:^{\mathrm{3}} {x}} \\ $$$$ \\ $$
Question Number 184791 Answers: 0 Comments: 2
$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{{e}^{{x}} +{e}^{−{x}} −\mathrm{2}}{{x}^{\mathrm{2}} } \\ $$
Question Number 184790 Answers: 2 Comments: 2
$${Evaluate} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+{x}\right)^{\mathrm{6}} −\mathrm{1}}{\left(\mathrm{1}+{x}\right)^{\mathrm{5}} −\mathrm{1}} \\ $$
Question Number 184787 Answers: 0 Comments: 2
$$\mathrm{x}^{\mathrm{4}} +\mathrm{16x}^{\mathrm{3}} +\mathrm{9x}^{\mathrm{2}} +\mathrm{256x}+\mathrm{256}=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}? \\ $$
Question Number 184775 Answers: 1 Comments: 2
$$\:\:\:\: \\ $$$$\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{6}\:+\:\frac{\mathrm{9}}{\mathrm{6}\:+\:\:\frac{\mathrm{25}}{\mathrm{6}\:\:+\:\:\frac{\mathrm{49}}{\mathrm{6}\:+\:\frac{\mathrm{81}}{\mathrm{6}+\:......}\:\:\:\:\:}\:\:\:\:\:}\:\:}\:\:\:\:\:\:\:\:}\:\:=? \\ $$$$ \\ $$$$ \\ $$
Question Number 184774 Answers: 1 Comments: 2
$${Calcul}\:{the}\:{sum} \\ $$$$\mathrm{1}.\Sigma{x}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$$\mathrm{2}.\Sigma{xarctan}\left({x}\right) \\ $$$$\mathrm{3}.\Sigma{e}^{{x}} {sinx} \\ $$$$\mathrm{4}.\Sigma\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{20}} \\ $$$$\mathrm{5}.\Sigma\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} \:}\:{a}>\mathrm{0} \\ $$$$\mathrm{6}.\Sigma{xsinx} \\ $$
Question Number 184773 Answers: 2 Comments: 1
$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{ax}+\mathrm{b}}{\:\sqrt{\mathrm{1}+\mathrm{3x}}−\mathrm{2}}=\mathrm{c} \\ $$$$\mathrm{2a}−\mathrm{2b}+\mathrm{3c}=? \\ $$$$\left(\mathrm{a},\mathrm{b},\mathrm{c}\right)\neq\mathrm{0} \\ $$$$\mathrm{pease}\:\mathrm{solution}???? \\ $$
Question Number 184769 Answers: 0 Comments: 2
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