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Question Number 186021 Answers: 1 Comments: 0
$${prove}\:{that}\left({using}\:{Epsilon}−{Delta}\:{definition}\right) \\ $$$$\left({a}\right)\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left(\mathrm{6}{x}−\mathrm{2}\right)=\mathrm{4} \\ $$$$\left({b}\right)\underset{{x}\rightarrow\mathrm{6}} {\mathrm{lim}}\sqrt{\mathrm{3}{x}−\mathrm{2}}=\mathrm{4} \\ $$
Question Number 186002 Answers: 1 Comments: 1
Question Number 185982 Answers: 1 Comments: 0
Question Number 185981 Answers: 1 Comments: 0
$$ \\ $$$$\:\:\:\:\:\:\:{solve}\:\:{in}\:\:\:\mathbb{R} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\lfloor\:\:\mathrm{2}{x}\:\rfloor\:\:+\:\lfloor\:\:\mathrm{3}{x}\:\rfloor\:=\:\mathrm{1} \\ $$$$\: \\ $$$$\:\:\:\:\lfloor\:{x}\:\rfloor\::=\:{greatest}\:{integer}\:{number} \\ $$$$\:\:\:\:{more}\:{than}\:\:{or}\:{equal}\:\:{to}\:\:''\:{x}\:'' \\ $$
Question Number 185983 Answers: 1 Comments: 0
$$ \\ $$$$\:\:\:\:\:\begin{cases}{\:\:\:{f}\::\:\:\left[\:\:\mathrm{0}\:\:,\:\:\mathrm{1}\:\right]\:\rightarrow\:\mathbb{R}}\\{\:\:\:\:{f}\:\left({x}\:\right)\:=\:\frac{\:\mathrm{4}^{\:{x}} }{\mathrm{2}\:+\:\mathrm{4}^{\:{x}} }}\end{cases} \\ $$$$\:\:\:\:\:\:{is}\:\:{given}\:.\:\:{find}\:{the}\:{value}\:{of} \\ $$$$\:\:\:\:\:\:{the}\:{following}\:{expression}. \\ $$$$\:\:\:\:\:\:\mathrm{E}\:=\:{f}\:\left(\frac{\mathrm{1}}{\mathrm{20}}\:\right)+\:{f}\left(\frac{\:\mathrm{2}}{\mathrm{20}}\:\right)+...\:+{f}\:\left(\frac{\mathrm{19}}{\mathrm{20}}\right)\:−{f}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\:\right)=? \\ $$
Question Number 185973 Answers: 1 Comments: 2
$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\left[\boldsymbol{{prove}}\:\boldsymbol{{that}};\right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:+\:\mathrm{2}\:=\:\mathrm{3} \\ $$$$ \\ $$
Question Number 185972 Answers: 1 Comments: 0
Question Number 185939 Answers: 0 Comments: 0
Question Number 185901 Answers: 0 Comments: 0
Question Number 185876 Answers: 3 Comments: 0
$${x}\:=\:\frac{\mathrm{2}{ab}}{{a}+{b}}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\: \\ $$$$\frac{{x}\:+\:{a}}{{x}\:−\:{a}}\:+\:\frac{{x}\:+\:{b}}{{x}\:−\:{b}}\:=\:\mathrm{2} \\ $$
Question Number 185840 Answers: 0 Comments: 1
Question Number 185843 Answers: 0 Comments: 1
Question Number 185842 Answers: 0 Comments: 1
Question Number 185780 Answers: 0 Comments: 0
$${find}\:{all}\:{solutions}\:{for} \\ $$$${k}!{m}!={n}! \\ $$$$\left({k},{m},{n}\in\mathbb{N}\right) \\ $$$$\left({m}\geqslant{k}>\mathrm{1}\right) \\ $$
Question Number 185760 Answers: 1 Comments: 0
$${A}=\mathrm{2}×\mathrm{10}^{\mathrm{0}} +\mathrm{10}^{−\mathrm{1}} +\mathrm{6}×\mathrm{10}^{−\mathrm{2}} +\mathrm{6}×\mathrm{10}^{−\mathrm{3}} +\mathrm{6}×\mathrm{10}^{−\mathrm{4}} +.... \\ $$$$\frac{{A}}{\mathrm{13}}=? \\ $$
Question Number 185747 Answers: 0 Comments: 0
Question Number 185744 Answers: 0 Comments: 0
Question Number 185734 Answers: 4 Comments: 0
$$\mathrm{x}\:=\:\sqrt{\mathrm{8}\:+\:\sqrt{\mathrm{40}\:+\:\mathrm{8}\:\sqrt{\mathrm{5}}}} \\ $$$$\mathrm{y}\:=\:\sqrt{\mathrm{8}\:−\:\sqrt{\mathrm{40}\:+\:\mathrm{8}\:\sqrt{\mathrm{5}}}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{x}^{\mathrm{6}} \:+\:\mathrm{y}^{\mathrm{6}} \:=\:? \\ $$
Question Number 185733 Answers: 0 Comments: 0
Question Number 185723 Answers: 1 Comments: 0
Question Number 185706 Answers: 3 Comments: 0
$$\mathrm{if}\:\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{find}:\:\:\:\:\:\mathrm{x}^{\mathrm{2011}} \:+\:\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2011}} }\:=\:? \\ $$
Question Number 185695 Answers: 2 Comments: 0
$${If}\:\overset{\rightarrow} {{u}}\:{and}\:\overset{\rightarrow} {{v}}\:{are}\:{vectors}\:{in}\:\mathbb{R}^{\mathrm{3}} \\ $$$${then}\:{prove}\:{that}\: \\ $$$$\overset{\rightarrow} {{u}}.\overset{\rightarrow} {{v}}=\frac{\mathrm{1}}{\mathrm{4}}\parallel\overset{\rightarrow} {{u}}+\overset{\rightarrow} {{v}}\parallel^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{4}}\parallel\overset{\rightarrow} {{u}}−\overset{\rightarrow} {{v}}\parallel^{\mathrm{2}} \\ $$
Question Number 185694 Answers: 0 Comments: 0
$${Show}\:{that}\:{the}\:{set}\:{V}=\mathbb{R}^{\mathrm{3}} \:{with} \\ $$$${standard}\:{vector}\:{addition}\:{and} \\ $$$${multiplication}\:{defined}\:{as} \\ $$$${c}\left({u}_{\mathrm{1}} ,{u}_{\mathrm{2}} ,{u}_{\mathrm{3}} \right)=\left(\mathrm{0},\mathrm{0},{cu}_{\mathrm{3}} \right) \\ $$
Question Number 185693 Answers: 1 Comments: 1
$$\mathrm{If}\:\:\:\mathrm{k}\:>\:\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{x}}{\mid\mathrm{x}\mid} \\ $$$$\mathrm{Find}\:\:\:\mathrm{f}\left(-\:\frac{\mathrm{2}}{\mathrm{7}}\:\mathrm{k}\right)\:+\:\mathrm{f}\left(\:-\:\mathrm{2k}\right)\:=\:? \\ $$
Question Number 185692 Answers: 0 Comments: 0
$${Given}\: \\ $$$$\overset{\rightarrow} {{u}}=\left(−\mathrm{2},\mathrm{3},\mathrm{1}\right)\:\:{and}\:\overset{\rightarrow} {{v}}=\left(\mathrm{7},\mathrm{1},−\mathrm{4}\right) \\ $$$${verify}\:{cauchy}−{schwartz}\: \\ $$$${inequarity}\:{and}\:{triangle}\:{inequarty} \\ $$
Question Number 185684 Answers: 0 Comments: 7
$$\mathrm{17}\:,\:\mathrm{78},\:\mathrm{143},\:\mathrm{353},\:? \\ $$$$\left.\mathrm{a}\left.\right)\left.\mathrm{3}\left.\mathrm{66}\:\:\:\:\:\mathrm{b}\right)\mathrm{0}\:\:\:\:\:\mathrm{c}\right)\mathrm{398}\:\:\:\:\:\mathrm{d}\right)\mathrm{435} \\ $$
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