All categories

3 years ago

The greatest integer function, shown below, is defined so that it produces the greatest integer __ or equal to x. f(x) = [ [x] ]

Mathematics

2 answers:

kap26 [50]3 years ago

8 0

Less than or equal to X :)

scoundrel [369]3 years ago

6 0

Less than or equal to x.

You might be interested in

(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

What is the equation of a line passing through (-2,3) and is perpendicular to the y-axis ?

Scrat [10]

Answer:

the answer is B

Step-by-step explanation:

4 0

4 years ago

Determine which score corresponds to the higher relative position. Which is better, a score of 92 on a test with a mean of 71 an

ss7ja [257]

Answer:

The score of 92 on a test with a mean of 71 and a standard deviation of 15 is better.

Step-by-step explanation:

To find which score corresponds to the higher relative position, we find the Z-score of each score.

The z-score, which measures how many standard deviation a measure is above or below the mean, is given by the following formula:

$Z = \frac{X - \mu}{\sigma}$

In which X is the score, $\mu$ is the mean and $\sigma$ is the standard deviation.

A score of 92 on a test with a mean of 71 and a standard deviation of 15.

So $X = 92, \mu = 71, \sigma = 15$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{92 - 71}{15}$

$Z = 1.4$

A score of 688 on a test with a mean of 493 and a standard deviation of 150.

So $X = 688, \mu = 493, \sigma = 150$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{688 - 493}{150}$

$Z = 1.3$

Which is better?

Due to the higher z-score, the score of 92 on a test with a mean of 71 and a standard deviation of 15 is better.

6 0

4 years ago

There are several characteristics of a parallelogram that can prove a quadrilateral is a parallelogram. Which characteristic wou

kirill [66]

The answer would be b

4 0

3 years ago

Read 2 more answers

The distance from the normal hairline to the base of the nose is equal to to the distance from the base of the chin to the

inn [45]

The answer is eyebrow. According to a research, the mean distance from chin to nose was 6.96 cm. The mean distance from nose to eyebrows was 6.55 cm. The mean space from eyebrows to hairline was 6.8 cm. while, the space from chin to hairline was 20.3 cm.

8 0

4 years ago