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4 years ago

How do you do this problem

Mathematics

1 answer:

Sliva [168]4 years ago

6 0

Answer:

Step-by-step explanation:

sec= x

cross multiply

60 mb x 2

120 mb/29 sec

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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

3 0

4 years ago

Phân tích : x^3+2x^2y+xy^2-9x

Galina-37 [17]

Answer:

x(x+y+3)(x+y-3)

Step-by-step explanation:

x³+2x²y+xy²-9x

= x((x²+2xy+y²)-3²)

= x((x+y)² - 3²)

= x(x+y+3)(x+y-3)

3 0

3 years ago

Which inequality matches the graph? <br> A) x 3 <br> C) x ≤ 3 <br> D) x ≥ 3

devlian [24]

The answer is C because you should look if it’s an open circle and which way the arrow is facing.

3 0

4 years ago

There are 38 students in Mr. Reynolds math class and 20 are boys.If a student is selected at random what is the probability that

damaskus [11]

Answer:

9/19

Step-by-step explanation:

if 20 students are boys, then the remaining students are girls. 38-20 = 18

There are 18 girl students.

18/38 can be simplified to 9/19

5 0

3 years ago

Read 2 more answers

Which number has a 4 whose value is 1/10 the value as the 4 in 645,792.38

Nookie1986 [14]

It would be 2. Have a nice day.

8 0

3 years ago