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
Help with question 17
Kruka [31]
Ok if you show me the question I can try to help but you got to show it
7 0
3 years ago
What is the answer to f(x)=x^2-10x+4 f(-2)
Maru [420]

Answer:

Step-by-step explanation:

f(x)=4+20+4

    =28

3 0
3 years ago
Jackson bought 3 pounds of candies for $9.75 What was the price of these candies in dollars per pound?
Stels [109]
9.75 dollars divided by 3 pounds equals 3.25 per pound
8 0
3 years ago
Help ASAP
Hoochie [10]
Don’t at me I think it’s B
5 0
3 years ago
The area of your new rectangular backyard is 3 1/8 square kilometers.The width of the new yard is 1/2 kilometers.What the length
m_a_m_a [10]
31/8 with in 1/2 in back yard
6 0
3 years ago
Other questions:
  • The rule which allows us to change the sign of an exponent is called the ____ rule.
    5·1 answer
  • The number k and 1.4 are additive inverses.
    14·1 answer
  • Solve the following inequality. Then place the correct answer in the box provided. Answer in terms of a mixed number.
    13·2 answers
  • Matthew was selling tacos at a rate of t=pn, where the total is equal to the price times the number sold. If each taco cost $8 a
    7·1 answer
  • Jack left a tip of $5.75 for his waiter. If this represents 20% of his meal, what was the cost, in dollars, of Jack’s meal witho
    7·1 answer
  • 6 x 10 5 is how many times the value of 3 x 10 (Hint: Write your answer in standard form.)​
    8·1 answer
  • Scott trained for the marathon.
    7·1 answer
  • Hey everyone I need help on the questions please!:)​
    7·1 answer
  • Justin is buying tickets to a concert online from Ticketmaster. He buys 3 tickets that all have the same price.
    12·1 answer
  • What is four times three?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!