Mathematics, 30.03.2020 23:12 kaiyerecampbell95
A subset $S \subseteq \mathbb{R}$ is called open if for every $x \in S$, there exists a real number $\epsilon > 0$ such that $(x-\epsilon, x \epsilon) \subseteq S$. A subset $T \subseteq \mathbb{R}$ is called closed if $\mathbb{R} \setminus T$ is open. (a) Show that an open interval is open and that a closed interval is closed. (b) Show that $\emptyset$ and $\mathbb{R}$ are the only subsets of $\mathbb{R}$ that are both open and closed. (This is very hard. At least try to convince yourself that $\emptyset$ and $\mathbb{R}$ are both open and closed. Showing there is no other set that is both open and closed is quite difficult.) (c) Show that an arbitrary union of open intervals is open. (d) Show that an arbitrary union of closed intervals need not be closed. (Hint: in light of the definition of closed, this is the same thing as showing that an arbitrary intersection of open intervals need not be open.)
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What is the simplified form of 7 √x • 7 √x • 7 √x • 7 √x?
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Mathematics, 21.06.2019 19:00
Simplify. −4x^2 (5x^4−3x^2+x−2) −20x^6−12x^4+8x^3−8x^2 −20x^6+12x^4−4x^3+8x^2 −20x^8+12x^4−4x^2+8x −20x^6+12x^4+4x^3−8x^2
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Mathematics, 21.06.2019 21:10
What is the domain of the given function? {(3,-2), (6, 1), (-1, 4), (5,9), (-4, 0); o {x | x= -4,-1, 3, 5, 6} o {yl y = -2,0, 1,4,9} o {x|x = -4,-2, -1,0, 1, 3, 4, 5, 6, 9} o y y = 4,-2, -1, 0, 1, 3, 4, 5, 6, 9}
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A subset $S \subseteq \mathbb{R}$ is called open if for every $x \in S$, there exists a real number...
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