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
Margarita [4]
3 years ago
5

Determine whether the integral is convergent or divergent. ∫[infinity] 2 e^−1/x / x^2 dx : O Convergent O divergent If it is con

vergent, evaluate it. (If the quantity diverges, enter DIVERGES.)
Mathematics
1 answer:
monitta3 years ago
8 0

Let f(x)=e^{-1/x}. Then f'(x)=\frac1{x^2}e^{-1/x}>0 for all x\ge2, so f is strictly increasing. As x\to\infty, e^{-1/x}\to e^0=1, so f is bounded above by 1. This is to say,

e^{-1/x}

and the integral of \frac1{x^2} converges over the same domain, so this integral must also converge by comparison.

We have, by setting y=-\frac1x,

\displaystyle\int_2^\infty\frac{e^{-1/x}}{x^2}\,\mathrm dx=\int_{-1/2}^0e^y\,\mathrm dy=e^0-e^{-1/2}=1-\frac1{\sqrt e}

You might be interested in
Can some help with this question
marissa [1.9K]

Answer:

y + 1 = 3(x - 1)

Step-by-step explanation:

The given point is (1,-1) meaning that x1 = 1 and y1 = -1

The slope of this line is m = 3 because we go up 3 and over to the right 1 (eg: go from the point (1,-1) to (2,2) to see this in action)

Plug these three pieces of info into the point slope formula below

y - y1 = m(x - x1)

y - (-1) = 3(x - 1)

y + 1 = 3(x - 1)

6 0
3 years ago
Read 2 more answers
if Janet spent 15 hours reading a 1,200 page book how many pages did Janet read per minute , round answer to decimal
Naddik [55]
1.3 pages first you take 15 * by 60 because 60 min. in one hour and then divide 1200 by 900 you get 1.3


8 0
3 years ago
Read 2 more answers
A sweater costs $33.23 and is subject to a 3.8% sales tax. What is the amount of the sales tax?
Tju [1.3M]
I believe that it’s $1.26 sales tax
5 0
3 years ago
Read 2 more answers
8. A banker's loan officer rates applications for credit. The rates are normally distributed with a mean of 200 and a standard d
masha68 [24]

Answer:

802

Step-by-step explanation:

3 0
3 years ago
Two numbers rolled can be added to get a sum. Find P(sum is even.)
azamat
When you roll two numbers you have four kinds of outcomes: EE, EO, OE, OO (where E = even, O = odd).

You get an even sum only if you sum two numbers that are both even or both odd, therefore the outcomes wanted are two: EE and OO.

Therefore:
P(sum is even) = 2 / 4 = 0.5

Hence, there is a 50% probability that, when you roll two numbers, their sum will be even.
6 0
3 years ago
Other questions:
  • What two integers is 70 between
    12·2 answers
  • If a material contains three elements joined in a fixed proportion, it is a(an)
    14·1 answer
  • A frustum is formed when a plane parallel to a cone’s base cuts off the upper portion as shown.
    7·2 answers
  • Bianca and Meredith are sisters. Meredith's height is 23 of Bianca's height plus 32 inches. Meredith is 60 inches tall. A girl i
    7·1 answer
  • Solve each equation for y
    9·1 answer
  • In general, the value measured by the vertical axis is called the _____ variable.
    10·2 answers
  • -6(2y + 3) + 6 = 24.
    9·1 answer
  • (0.a * 10) - (0.a ÷ 10) = 6.93
    8·2 answers
  • Janeece built a rectangular garden bed that was 14
    5·1 answer
  • Irfan exited his apartment building
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!