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Eva8 [605]
4 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]4 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.

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Which is true about the completely simplified difference of the polynomials a3b + 9a2b2 − 4ab5 and a3b − 3a2b2 + ab5?
Mrrafil [7]

Answer:

The difference is a binomial with a degree of 6

Step-by-step explanation:

Given:

a^3b + 9a^2b^2 − 4ab^5 and a^3b − 3a^2b^2 + ab^5

Let A = a^3b + 9a^2b^2 - 4ab^5

B= a^3b - 3a^2b^2+ab^5

The difference between A and B is

A - B = a^3b + 9a^2b^2 - 4ab^5 - (a^3b - 3a^2b^2 + ab^5)

Open parenthesis

A - B= a^3b + 9a^2b^2 - 4ab^5 - a^3b + 3a^2b^2 - ab^5

= a^3b - a^3b + 9a^2b^2 + 3a^2b^2 - 4ab^5 - ab^5

= 12a^2b^2 - 5ab^5

The fist term 12a^2b^2 has 2+2=4 as a degree

The second term 5ab^5 has 1 +5 =6 as a degree

Therefore,

the answer is: The difference is a binomial with a degree of 6

3 0
3 years ago
A music store is offering a Frequent Buyers Club membership. The membership costs $22 per year, and then a member can buy CDs at
sammy [17]

Answer:the cost of each CD for a member is $5.25

Step-by-step explanation:

The membership costs $22 per year, and then a member can buy CDs at a reduced price.

Let x represent the cost of each CD for a member.

Let n represent the number of CDs that each member buys. This means that the total cost of buying n CDs for a member for a year would be

22 + nx

If a member buys 17 CDs in one year, the cost is $111.25. This means that

17x + 22 = 111.25

17x = 111.25 - 22 = 89.25

x = 89.25/175 = 5.25

6 0
3 years ago
Three-fourths of a research team worked in a lab while one-fourth of the team worked near a pond. Of the researchers who worked
Lisa [10]

Answer:

3.5%

Step-by-step explanation:

In this case, the final probability would be the product of the two probabilities that the plating shows us:

First probability would be:

We are told that three quarters of the equipment (3/4) in the laboratory and the other quarter (1/4) near the pond, we are interested in the latter, that is, the probability is 1/4 = 0.25

Second probability:

We are told that 14% collected insects, therefore it would be 0.14

The final product is the question they ask us:

0.25 * 0.14 = 0.035

Which means that the joint probability is 3.5%

8 0
3 years ago
Solve for x PLZ HELP!!!
r-ruslan [8.4K]

21


3 times 5 =15

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3 0
4 years ago
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Please see the question attached and pleaaasssseeeeeeeee help god will bless youu
patriot [66]
I think You should break it down to the First and third One because of

7 0
4 years ago
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