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Svetach [21]
3 years ago
15

Please calculate this limit please help me​

Mathematics
1 answer:
Tasya [4]3 years ago
7 0

Answer:

We want to find:

\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n}

Here we can use Stirling's approximation, which says that for large values of n, we get:

n! = \sqrt{2*\pi*n} *(\frac{n}{e} )^n

Because here we are taking the limit when n tends to infinity, we can use this approximation.

Then we get.

\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n} = \lim_{n \to \infty} \frac{\sqrt[n]{\sqrt{2*\pi*n} *(\frac{n}{e} )^n} }{n} =  \lim_{n \to \infty} \frac{n}{e*n} *\sqrt[2*n]{2*\pi*n}

Now we can just simplify this, so we get:

\lim_{n \to \infty} \frac{1}{e} *\sqrt[2*n]{2*\pi*n} \\

And we can rewrite it as:

\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n}

The important part here is the exponent, as n tends to infinite, the exponent tends to zero.

Thus:

\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n} = \frac{1}{e}*1 = \frac{1}{e}

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Which is the equation of a line that has a slope of -2/3 and passes through point (-3, -1)? y=-2/3x+1.
bazaltina [42]

Answer:

y = -2/3x - 3

Step-by-step explanation:

First, write the equation using the slope. It should look like this: y = -2/3x + b. Next, find the y intercept by plugging in the point. This is what it looks like: -1 = -2/3(-3) + b. Multiply -2/3 by -3 to get 2. This is what it should look like now: -1 = 2 + b. Subtract 3 from both sides to get -3 = b. Go back to your original equation and plug in -3 for b. This is your final equation:

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Hope this helped! :)

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STOOPID

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HELP ME QUICK PLEASEE!!
Lena [83]

Answer:

  A) is a function

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Step-by-step explanation:

A) Yes, the relation is a function.

A function has a unique input value for each output value. There are no repeated x-values, so this relation is a function.

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B) The table says y=6 for x=6.

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C) Substituting the given information, we have ...

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