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]
2 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:
monitta2 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
Slove by using elimination <br> 3x+7y=27 <br> -3x+y=21
tankabanditka [31]

Answer:

x = -5

y = 6

Step-by-step explanation:

3x + 7y = 27      --------------(I)

-3x + y = 21        -----------(II)

Add equation (I) & (II) and so x will be eliminated and we can find the value of y.

(I)      3x + 7y = 27    

(II)    <u> -3x + y = 21  </u>      {add}

                8y = 48

                   y = 48/8

                   y = 6

Plugin y = 6 in equation (I)

3x +7*6 = 27

3x + 42 = 27

       3x = 27 - 42

       3x = -15

         x = -15/3

x = -5

8 0
3 years ago
How could you find the slope on a coordinate graph?
Irina18 [472]
Rise over run or how much it goes up or down over how much it goes left or right

4 0
3 years ago
The average weight of an adult blue whale is 365.000 pounds. Which expression represents this weight in scientific notation? A)
Elina [12.6K]
The answer is 3.65 x 10^5
7 0
2 years ago
The cost of hiring a surfboard involves an up-front fee plus an hourly rate. Three hours of hire costs $50 and 7 hours costs $90
siniylev [52]

Answer:

...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 0
3 years ago
Write the equation of the line that is perpendicular to y = 2x - 4 that goes through
user100 [1]

Answer:

y = 2x + 13

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Other questions:
  • Stephen had 24 miniature cars. He gave 2 cars to his brother. Then he passed the rest of the cars equally among 4 friends. Which
    15·1 answer
  • Which of the following is the largest volume? 4.5 x 102 m3 4.5 x 107 cm3 4.5 x 104 dm3 5.0 x 108 mm3 (the 100's are actually 10^
    14·1 answer
  • A scale on a map shows that 2.52, 5 centimeters = 15 kilometers. What number of actual kilometers are represented by 17.5 centim
    8·1 answer
  • A color printer prints 25 pages in 10 minutes. How many pages does it print per minute
    7·2 answers
  • How do you verify factoring is correct?
    6·1 answer
  • A. 12<br> B. 10<br> C. 6<br> D. 5
    8·1 answer
  • How do I do this? Please help me
    7·1 answer
  • During a sale, every item in a store is 80% of its regular price. 1.If the regular price of a T-shirt is$10, what is its sale pr
    5·2 answers
  • Toni can carry up to 19 lb in her backpack. Her lunch weighs 1 lb, her gym clothes weigh 2 lb, and her books (b) weigh 4 lb each
    9·1 answer
  • I NEED HELP RIGHT AWAY!!!! I'LL GIVE YOU 30 POINTS AND TRY TO MARK YOU AS BRAINLIST.Q: What do you need to do to the equations s
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!