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trasher [3.6K]
3 years ago
6

Find the values of p for which the following integral converges:

Mathematics
1 answer:
sweet [91]3 years ago
7 0

Answer:

Step-by-step explanation:

Find the values of p for which the following integral converges:

∫[infinity]e 1/(x(ln(x))^p)dx

Input youranswer by writing it as an interval. Enter brackets or parentheses in the first and fourth blanks as appropriate, and enter the interval endpoints in the second and third blanks. Use INF and NINF (in upper-case letters) for positive and negative infinity if needed. If the improper integral diverges for all p, type an upper-case "D" in every blank.

​Values of p are in the interval ,

For the values of p at which the integral converges, evaluate it. Integral =

Recall that

\int\limits^{\infty}_1 \frac{1}{x^p}  dx

converge if p > 1  and converge to \frac{1}{p-1} and divertgent if p ≤ 1

Now, let u = Inx ⇒ du = 1/x dx

: e ≤ x ≤ ∞ ⇒ 1 ≤ u < ∞

⇒ \int\limits^{\infty}_e \frac{dx}{x(Inx)^p} = \int\limits^{\infty}_1 {x} \frac{du}{u^p}

converge if p > 1  and converge to \frac{1}{p-1} and divertgent if p ≤ 1

\text {Integral}=\frac{1}{p-1}

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Please help and thank you
kondaur [170]

Answer:

Step-by-step explanation:

Let's see how well I can explain this. \frac{\pi}{6} is the same as a 30 degree angle which is in quadrant 1. If you picture the unit circle, right in the center of it is the origin. If you draw a straight line from 30 degrees and through the center (the origin), you will automatically "connect" with the reference angle of 30 (this is true for ALL angles on the unit circle). This puts us in quadrant 3. In quadrant 3, x is negative and so is y. So the terminal point of the reference angle for 30 degrees has the same exact values, but both of them are negative (again, because both x and y are negative in quadrant 3). I can't see your choices but the one you want looks like this:

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3 0
2 years ago
Douglas invests money in two simple interest accounts. He invests three times as much in an account paying 14% as he does in an
Rainbow [258]

Douglas invested $ 1300 altogether

<em><u>Solution:</u></em>

Let x represent the amount invested in the account paying 14% interest.

Let y represent the amount invested in the account paying 5% interest

He invests three times as much in an account paying 14% as he does in an account paying 5%

Which means,

x = 3y

<em><u>The simple interest is given by formula:</u></em>

S.I = \frac{p \times n \times r}{100}

Where,

"p" is the principal

"n" is the number of years

"r" is the rate of interest

<em><u>He earns $152.75 in interest in one year from both accounts combined</u></em>

Therefore,

Combined S.I = 152.75

n = 1 year

<em><u>Considering the account earning 14% interest:</u></em>

S.I = \frac{3y \times 14 \times 1}{100}\\\\S.I = 0.42y

<em><u>Considering the account earning 5% interest:</u></em>

S.I = \frac{y \times 5 \times 1}{100}\\\\S.I = 0.05y

<em><u>Since, Combined S.I = 152.75</u></em>

Therefore,

0.42y + 0.05y = 152.75

0.47y = 152.75

Divide both sides by 0.47

y = 325

Therefore,

x = 3y

x = 3(325)

x = 975

<em><u>how much did he invest altogether?</u></em>

Amount invested together = x + y = 975 + 325 = 1300

Thus he invested $ 1300 altogether

3 0
3 years ago
the library, post office, and gas station are all on elm street. the library is three miles west of the post office. the gas sta
Paha777 [63]

Answer:

distance apart= 9 miles

Step-by-step explanation:

The library , post office and gas station are all on elm street. The library is 3 miles away westward of the post office. The gas station is also 6 miles east of the post office. The distance between the library and the gas station can be computed below.

The post office is located at the middle between the library and the gas station. The library goes 3 miles westward of the post office while the gas station goes 6 miles eastward of the post office. The distance apart between the library and the gas station is the sum of the distance of the gas station from the post office and the distance of the library from the post office .

Therefore,

6miles  + 3 miles = 9 miles

7 0
3 years ago
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