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lidiya [134]
3 years ago
13

50 points

Mathematics
1 answer:
NISA [10]3 years ago
4 0
1. Using your straightedge, draw a reference line, if one is not provided.
2. Copy the side of the square onto the reference line, starting at a point labeled A'.
3. Construct a perpendicular at point B' to the line through ab2.
4. Place your compass point at B', and copy the side of the square onto the perpendicular b'g. Label the end of the segment copy as point C.
5. With your compass still set at a span representing AB, place the compass point at C and swing an arc to the left.
6. Holding this same span, place the compass point at A' and swing an arc intersecting with the previous arc. Label the point of intersection as D.
7. Connect points A' to D, D to C, and C to B' to form a square.
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Find the number to which the sequence {(3n+1)/(2n-1)} converges and prove that your answer is correct using the epsilon-N defini
Nat2105 [25]
By inspection, it's clear that the sequence must converge to \dfrac32 because

\dfrac{3n+1}{2n-1}=\dfrac{3+\frac1n}{2-\frac1n}\approx\dfrac32

when n is arbitrarily large.

Now, for the limit as n\to\infty to be equal to \dfrac32 is to say that for any \varepsilon>0, there exists some N such that whenever n>N, it follows that

\left|\dfrac{3n+1}{2n-1}-\dfrac32\right|

From this inequality, we get

\left|\dfrac{3n+1}{2n-1}-\dfrac32\right|=\left|\dfrac{(6n+2)-(6n-3)}{2(2n-1)}\right|=\dfrac52\dfrac1{|2n-1|}
\implies|2n-1|>\dfrac5{2\varepsilon}
\implies2n-1\dfrac5{2\varepsilon}
\implies n\dfrac12+\dfrac5{4\varepsilon}

As we're considering n\to\infty, we can omit the first inequality.

We can then see that choosing N=\left\lceil\dfrac12+\dfrac5{4\varepsilon}\right\rceil will guarantee the condition for the limit to exist. We take the ceiling (least integer larger than the given bound) just so that N\in\mathbb N.
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3 years ago
What is 4 1/2 times 3
Leya [2.2K]

Answer:

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Step-by-step explanation:

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2 years ago
48.7 simplified is...?<br><br> 48.7 =~ ???
son4ous [18]
As a fraction it’s 48 7/10
As a percentage it’s 4870%
Hope that helped!
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Solve for x:|3x + 12|=18
inessss [21]
|3x+12|=18\iff3x+12=18\ or\ 3x+12=-18\\subtract\ 12\ from\ both\ sides\\\\3x=6\ or\ 3x=-30\ \ \ \ |divide\ both\ sides\ by\ 3\\\\\huge\boxed{x=2\ or\ x=-10}
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3 years ago
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