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Question Number 166911 Answers: 1 Comments: 0
Question Number 166910 Answers: 1 Comments: 1
$${given}\:{that}\:{is}\:{prime},{proof}\:{that}\:\sqrt{{p}}\:{is}\: \\ $$$${irrational} \\ $$
Question Number 166904 Answers: 1 Comments: 0
$${A}\:{pendulum}\:{has}\:{a}\:{period}\:\mathrm{2}{sec}.\:{The} \\ $$$${bob}\:{pulled}\:{aside}\:{a}\:{distance}\:\mathrm{8}{cm}\:{as} \\ $$$${the}\:{amplitude}\:{and}\:{release}.\:{Find}\:{the} \\ $$$${displacement}\:{of}\:{the}\:{bob}\:\mathrm{0}.\mathrm{7}{sec}\:{after} \\ $$$${it}\:{has}\:{been}\:{released}. \\ $$
Question Number 166881 Answers: 0 Comments: 0
Question Number 166922 Answers: 0 Comments: 0
$$\mathrm{calculate}\:\::\:\:\:\underset{\mathrm{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\left(\mathrm{1}+\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}} −\mathrm{4}}{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} }=\mathrm{ln16}−\mathrm{3} \\ $$
Question Number 166921 Answers: 0 Comments: 1
Question Number 166875 Answers: 2 Comments: 1
Question Number 166872 Answers: 2 Comments: 0
$$ \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{e}^{\:−{x}} .{ln}\left({x}\right).{sin}\left({x}\right)}{{x}}\:{dx}\:=\:−\frac{\pi}{\mathrm{8}}\:\left(\mathrm{2}\gamma\:+\:{ln}\left(\mathrm{2}\right)\right) \\ $$$$ \\ $$
Question Number 166861 Answers: 3 Comments: 7
Question Number 166839 Answers: 1 Comments: 0
$$\int_{−{oo}} ^{+{oo}} \frac{{xe}^{{x}} }{\left(\mathrm{1}+{e}^{{x}} \right)^{\mathrm{2}} }{dx} \\ $$
Question Number 166834 Answers: 2 Comments: 0
Question Number 166830 Answers: 1 Comments: 0
Question Number 166829 Answers: 1 Comments: 0
$$ \\ $$$$\:\:\:\:\:\:\:\:{calculate}\: \\ $$$$\:\:\:\mathrm{I}{f}\:,\:\:\:\:{f}\left({x}\right)=\frac{\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt[{\mathrm{3}}]{\left({x}^{\:\mathrm{2}} +{x}−\mathrm{2}\right)\left({x}^{\:\mathrm{4}} −\mathrm{1}\right)\left({x}^{\:\mathrm{2}} +\mathrm{2}{x}−\mathrm{3}\right)+\mathrm{16}}\:\:+\:\sqrt{{x}^{\:\mathrm{2}} +\mathrm{3}}}{\left(\:\mathrm{1}+{x}\:+{x}^{\:\mathrm{2}} \right)} \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{then}\:,\:\:\:\:{f}\:'\:\left(\mathrm{1}\:\right)\:=?\:\:\:\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n} \\ $$$$ \\ $$
Question Number 166828 Answers: 0 Comments: 0
$$\mathrm{calculate}:\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{n}+\mathrm{k}^{\alpha} }\:\:\:\:\:\:\:\:\:\:\:\:.\left(\mathrm{0}<\alpha<\mathrm{1}\right) \\ $$
Question Number 166822 Answers: 1 Comments: 0
Question Number 166818 Answers: 1 Comments: 3
Question Number 166814 Answers: 2 Comments: 0
$${f}\left({x}\right)={x}^{{n}} {e}^{−{nx}} \\ $$$${Determinate}\:{f}^{\left({n}\right)} \left({x}\right). \\ $$
Question Number 166813 Answers: 2 Comments: 0
$${f}\left({x}\right)={x}^{\mathrm{2}{n}} \\ $$$${Determinate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$
Question Number 166812 Answers: 0 Comments: 0
$${f}\left({x}\right)={e}^{{nx}} {cos}\left({x}\right). \\ $$$${Determinate}\:{f}^{\left({n}\right)} \left({x}\right). \\ $$
Question Number 166805 Answers: 1 Comments: 0
$${f}\left({x}\right)=\frac{{x}}{\mathrm{1}+\mid{x}\mid}. \\ $$$${show}\:{that}\:\exists\:{K}\:\in\:\mathbb{R}_{+} \:{such}\:{that} \\ $$$$\forall\:{x},\:{y}\:\in\:\mathbb{R},\:\mid{f}\left({x}\right)−{f}\left({y}\right)\mid\leqslant{K}\mid{x}−{y}\mid \\ $$
Question Number 166801 Answers: 1 Comments: 2
$${Calculate}: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{x}−\sqrt{{x}}}{\:\sqrt[{\mathrm{3}}]{{sin}\left({x}\right)−{tan}^{\mathrm{2}} \left({x}\right)}} \\ $$
Question Number 166888 Answers: 1 Comments: 0
Question Number 166892 Answers: 2 Comments: 0
$$ \\ $$$$\:\:\:{solve}\:{in}\:\:\mathbb{R} \\ $$$$ \\ $$$$\:\:{i}:\:\:\:\:\lfloor\:{x}\:\lfloor\:{x}\rfloor\rfloor=\:\mathrm{3}{x} \\ $$$$ \\ $$$$\:\:{ii}\::\:\:\:\lfloor{x}\:\rfloor^{\:\mathrm{2}} −\mathrm{3}\:\lfloor{x}\:\rfloor\:+\mathrm{2}\:\leqslant\:\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:−−−−−− \\ $$$$ \\ $$
Question Number 166891 Answers: 0 Comments: 0
$${Linearize}\:{sin}^{\mathrm{4}} \left({x}\right){cos}^{\mathrm{2}} \left({x}\right) \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$
Question Number 166796 Answers: 1 Comments: 0
$$\:\:\:\:\int\:\frac{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}}{\left(\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{1}\right)\sqrt{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{1}}}\:\mathrm{dx} \\ $$
Question Number 166793 Answers: 1 Comments: 0
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