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HACTEHA [7]
3 years ago
6

What is an equation of the line that passes through the points (8,2) and (7,1)?

Mathematics
1 answer:
gogolik [260]3 years ago
8 0

Answer:

Step-by-step explanation:

first, we find the slope

slope = (y2 - y1) / (x2 - x1)

(8,2)....x1 = 8 and y1 = 2

(7,1)....x2 = 7 and y2 = 1

now we sub

slope = (1 - 2) / (7 - 8) = -1/-1 = 1

y = mx + b

slope(m) = 1

use either of ur points...I will use (8,2)...x = 8 and y = 2

now we sub and find b, the y intercept

2 = 1(8) + b

2 = 8 + b

2 - 8 = b

-6 = b

so ur equation is : y = 1x - 6....or just y = x - 6 <===

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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:

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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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3 years ago
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Step-by-step explanation:

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