1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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}

You might be interested in
Use the probability distribution table to answer the question.
dalvyx [7]

Answer:

0.88

Step-by-step explanation:

P(x≥2) = P(x=2) + P(x=3) + P(x=4) + P(x=5) + P(x=6)

P(x≥2) = 0.21 + 0.35 + 0.21 + 0.06 + 0.05

P(x≥2) = 0.88

Or, you can calculate it as:

P(x≥2) = 1 - P(x=1) - P(x=0)

P(x≥2) = 1 - 0.09 - 0.03

P(x≥2) = 0.88

7 0
3 years ago
PLEASE HELP PLEASE URGENT!!
vovangra [49]

Answer:

B) 1,260

Step-by-step explanation:

7!/2!2! = 1,260

5 0
2 years ago
What number must be added to both sides of the equation to complete the square ?
77julia77 [94]
First consider (x+c)^2 where c is just a random constant. if we expand this by foil (which is distributive property twice), we get x^2 + 2cx+ c^2. we want to find c^2 and to do that, we can first find c. we can find c by looking at the 2cx term. this term should match with 12x, so therefore 2c = 12 so c = 6. this also implies that c^2 = 36.
note that for this problem i was working backwards which is a very powerful problem solving tool: start with what you want to attain, and then see how you can go from where you are now to get to your destination.

let me know if you have any questions!!!

7 0
3 years ago
Assume that a spherical cell, with a diameter of 18 μm, has spherical mitochondria, each with a diameter of 0.18 μm. If mitochon
laiz [17]

Since the linear dimension of the mitochondria is 10^-2 times that of the cell, the volume as a proportion of cell volume will be (10^-2)^3 = 10^-6. In order to make up 0.134 of the cell volume, there must be

(1.34×10^-1)/(10^-6) = 1.34×10^5

mitochondria in the cell.

There are about 134,000 mitochondria.

4 0
3 years ago
Find the surface area of the right rectangular prism shown below. units²
faust18 [17]

Answer:

67 units^2

Step-by-step explanation:

The surface area of the prism is found by

SA = 2 ( lw+lh + wh)

     = 2 ( 5*1.5+ 4*1.5 + 5*4)

     = 2 ( 7.5+6+20)

     = 2 (33.5)

    = 67

5 0
3 years ago
Read 2 more answers
Other questions:
  • How do you find the solutions of the equation 2sin^2(x)=1
    5·1 answer
  • Which is the graph of y= cos(x-pi)
    10·1 answer
  • 13/14 make it in to a equivalent fraction​
    6·1 answer
  • Yoshi saved $5 each week for 23 weeks. What is the total amount of money he saved. Use an area model to solve
    13·1 answer
  • If the mean of 6 numbers increased by 3, by how much would the sum of
    8·1 answer
  • I NEED HELP ASAP
    6·1 answer
  • Write an inequality that represents the graph.
    5·1 answer
  • SOMEONE HELP ASAP!!
    5·1 answer
  • Which of the following can be used to evaluate the series?
    9·1 answer
  • As an estimation we are told 5 miles is 8 km. Convert 10 miles to km.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!