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3 years ago

If F(x) = 2x^ln(x), then F'(2) =

Mathematics

2 answers:

joja [24]3 years ago

8 0

2=3x4m3Aojsksh=20jsjsjsjshxoxdd

pantera1 [17]3 years ago

7 0

Answer:

eln2(x)ln(x4)/x

I HOPE THIS HELPED!

Step-by-step explanation:

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An integer is chosen random between 1 to 100. find the probability that it is divisible by 8

arlik [135]

Answer: 0.12

x is the number which is chosen

The number of ways to choose x from 1 to 100 is 100 (ways)

because x is divisible by 8 => x ∈ {8; 16;...; 96}

=> the number of terms divisible by 8 from 1 to 100 is (96 - 8)/8 + 1 = 12

the number of ways to choose x which is divisible by 8 is 12 (ways)

=> the probability that x is divisible by 8 is 12/100 = 0.12

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Let f be defined by the function f(x) = 1/(x^2+9)

riadik2000 [5.3K]

(a)

$\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}$

Substitute x = 3 tan(t ) and dx = 3 sec²(t ) dt :

$\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt$

$=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}$

(b) The series

$\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}$

converges by comparison to the convergent p-series,

$\displaystyle\sum_{n=3}^\infty\frac1{n^2}$

$\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}$

converges absolutely, since

$\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}$

That is, ∑ (-1)ⁿ (n ² + 9)/eⁿ converges absolutely because ∑ |(-1)ⁿ (n ² + 9)/eⁿ| = ∑ (n ² + 9)/eⁿ in turn converges by comparison to a geometric series.

5 0

3 years ago

1. How many parts have the same color? 2. Identify the colors that occupies the first three largest part.

Jlenok [28]

9514 1404 393

Answer:

no parts have the same color (0)
yellow, blue, red
percentages can be written in several forms: fraction, decimal, for example. The sectors can also be identified by their angle measures.
see attached

Step-by-step explanation:

1. The seven different sectors have seven different colors. No parts have the same color.

2. The attached table lists the sectors in decreasing order of size. The largest three are yellow, blue, red.

3. Percentages can be written a number of ways. They can be written as decimal numbers, or as fractions. In a pie chart, the sectors can also be given an angle measure.

4. Fraction equivalents of the percentages are shown in the attached.

5. Reduce fraction equivalents of the percentages are shown in the attached.