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Rina8888 [55]
3 years ago
10

Rewrite the function f(x)=7 (1/2)^3x using the properties of exponents.

Mathematics
1 answer:
Nutka1998 [239]3 years ago
3 0

Answer:

f(x) = (7 x)\/8

Step-by-step explanation:

idk, i just used wolframalpha mate...

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Please calculate this limit <br>please help me​
Tasya [4]

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}

7 0
3 years ago
Rachel babysits the Michaelson’s kids on Saturdays for 4 hours and is paid $12.50 per hour. On Sundays, she babysits at the Smit
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She earns $8.00 more on Sunday

Step-by-step explanation:

Saturday 12.50x4=50.00

Sunday 14.50x4=58.00

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