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
Eva8 [605]
3 years ago
13

Determine whether each integral is convergent or divergent. If it is convergent evaluate it. (a) integral from 1^(infinity) e^(-

2x) dx. (b) integral from 1^2[dz]/[(z-1)^2] . (c) integral from 1^(infinity) [dx]/[root(x)] .
Mathematics
1 answer:
AVprozaik [17]3 years ago
4 0

Answer:

a) So, this integral is convergent.

b) So, this integral is divergent.

c) So, this integral is divergent.

Step-by-step explanation:

We calculate the next integrals:

a)

\int_1^{\infty} e^{-2x} dx=\left[-\frac{e^{-2x}}{2}\right]_1^{\infty}\\\\\int_1^{\infty} e^{-2x} dx=-\frac{e^{-\infty}}{2}+\frac{e^{-2}}{2}\\\\\int_1^{\infty} e^{-2x} dx=\frac{e^{-2}}{2}\\

So, this integral is convergent.

b)

\int_1^{2}\frac{dz}{(z-1)^2}=\left[-\frac{1}{z-1}\right]_1^2\\\\\int_1^{2}\frac{dz}{(z-1)^2}=-\frac{1}{1-1}+\frac{1}{2-1}\\\\\int_1^{2}\frac{dz}{(z-1)^2}=-\infty\\

So, this integral is divergent.

c)

\int_1^{\infty} \frac{dx}{\sqrt{x}}=\left[2\sqrt{x}\right]_1^{\infty}\\\\\int_1^{\infty} \frac{dx}{\sqrt{x}}=2\sqrt{\infty}-2\sqrt{1}\\\\\int_1^{\infty} \frac{dx}{\sqrt{x}}=\infty\\

So, this integral is divergent.

You might be interested in
What is the diffrance -2-8
kow [346]
-10 is the answer yuhhhhh
7 0
2 years ago
The sum of what integer and 181 is equal to -236?
slavikrds [6]

Answer:

<h2>- 417</h2>

Step-by-step explanation:

n - integer

The sum of n and 181 is equal to -236:

n + 181 = -236              <em>subtract 181 from both sides</em>

n + 181 - 181 = -236 - 181

n = -417

6 0
3 years ago
Factoring the expression 15x+6 using GCF
s344n2d4d5 [400]
The answer is 3(5x+2) i hope this helps you.
3 0
3 years ago
Cameroon was paid $173.70 for working 18 hours. how much money does he make per hour?
PilotLPTM [1.2K]
Since you are looking for the dollar per hour, can just set the equation up as dollar divided by hour (dollar/hour). You take how much was made ($173.70) and divide it by the hours worked (18 hours).

$173.70/18 = x (x representing how much he makes an hour).

$173.70/18 = $9.65.

Cameroon makes $9.65 an hour.
6 0
3 years ago
Look at picture (15 point)
NNADVOKAT [17]

Answer:

<h2>x \sqrt{2}</h2>

Option C is the correct option

Step by step explanation

\sqrt{ \frac{22 {x}^{6} }{11 {x}^{4} } }

Reduce the fraction with 11

\sqrt{ \frac{2 {x}^{6} }{ {x}^{4} } }

Simplify the expression

\sqrt{2 {x}^{6 - 4} }

\sqrt{2  \: {x}^{2} }

Simplify the radical expression

x \sqrt{2}

Hope this helps...

Good luck on your assignment..

3 0
3 years ago
Other questions:
  • It take Anna 45 minutes to walk 2 1/2 miles to the park. At this rate, how many minutes should it take her to walk 3 miles?
    14·1 answer
  • What two expressions represent 3/12​
    14·1 answer
  • Which equations are related equations to x + 8 = 22?
    13·1 answer
  • What is y=1.1(x-5.8)^2+5.2 in standard form
    11·1 answer
  • I NEED HELP!! thank u;-)
    11·2 answers
  • use the numbers 1-10 to fill in the blanks and find the length of the hypotenuse. Can you find any combination that creates a in
    12·1 answer
  • Line Q is represented by the following equation: 2x + y = 11
    15·2 answers
  • Luis has some nickels, dimes, and quarters. The value of all of the coins, in cents, is represented with the expression shown.
    7·1 answer
  • What is the distance between a and b <br>a 45<br>b 20<br>c 25<br>d 60​
    5·1 answer
  • How do I do this question?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!