3 years ago

1 4 cm 4 cm 5 cm 3 cm Perimeter: Area:

Mathematics

1 answer:

ohaa [14]3 years ago

7 0

Answer:

Step-by-step explanation:

840

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lisov135 [29]

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(1 pt) Let an=n+1n+3. Find the smallest number M such that: (a) |an−1|≤0.001 for n≥M M= 1997 (b) |an−1|≤0.00001 for n≥M M= 20000

xenn [34]

We want to prove

$\displaystyle\lim_{n\to\infty}\frac{n+1}{n+3}=1$

which is akin to saying that, for any given $\varepsilon>0$ , we guarantee that

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

for all $n$ exceeding some threshold $N=N(\varepsilon)$ .

We want to end up with

$\left|\dfrac{n+1}{n+3}-1\right|=\left|-\dfrac2{n+3}\right|=\dfrac2{n+3}$

$\implies\dfrac{n+3}2>\dfrac1\varepsilon\implies n>\dfrac2\varepsilon-3$

which suggests that we guarantee that $a_n$ is arbitrarily close to 1 if $N=\left\lceil\dfrac2\varepsilon-3\right\rceil$ . (Take the ceiling to ensure $N$ is a natural number.)

Now for the proof: Let $\varepsilon>0$ be given. Then for $n>N=\left\lceil\dfrac2\varepsilon-3\right\rceil$ we have

$n>\left\lceil\dfrac2\varepsilon-3\right\rceil\le\dfrac2\varepsilon-3\implies\dfrac2{n+3}$

QED

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Whats a multiplication problem with a product of 5 to the 13th power

fredd [130]

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3 years ago

The base of the triangle is one and a half times it's height. what is height if area is 75

Setler [38]

H=15cm
b=10cm
i think, i asked my mom thats a teacher and she said it was correct.

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3 years ago

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1 4 cm 4 cm 5 cm 3 cm Perimeter: Area:​

1 4 cm 4 cm 5 cm 3 cm Perimeter: Area: