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schepotkina [342]
3 years ago
8

Find the value of the integral that converges. ∫^-5_-[infinity] x^-2 dx.

Mathematics
1 answer:
Bingel [31]3 years ago
8 0

Answer:

\int_{-\infty}^{-5} x^{-2}dx= \frac{1}{5} + \lim_{x\to -\infty} \frac{1}{x} =\frac{1}{5}

Because the \lim_{x\to -\infty} \frac{1}{x} =0

The integral converges to \frac{1}{5}

Step-by-step explanation:

For this case we want to find the following integral:

\int_{-\infty}^{-5} x^{-2}dx

And we can solve the integral on this way:

\int_{-\infty}^{-5} x^{-2}dx= \frac{x^{-2+1}}{-2+1} \Big|_{-\infty}^{-5}

\int_{-\infty}^{-5} x^{-2}dx= -\frac{1}{x} \Big|_{-\infty}^{-5}

And if we evaluate the integral using the fundamental theorem of calculus we got:

\int_{-\infty}^{-5} x^{-2}dx= \frac{1}{5} + \lim_{x\to -\infty} \frac{1}{x} =\frac{1}{5}

Because the \lim_{x\to -\infty} \frac{1}{x} =0

The integral converges to \frac{1}{5}

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DaniilM [7]

Answer:

c.

Step-by-step explanation:

Plug in -2 for x ....

f(x) = -2^3 - 7(-2)^2 + 3

     = -8 - 28 + 3

     = -36 + 3

     = -33

Plug in 3/4 for x ....

f(x) = 3/4^3 - 7(3/4)^2 + 3

     = 27/64 - 63/16 + 3

The put in decimals ....

27/64 = .422

63/16 = 3.938

Put the decimals back into the equation ....

     = .422 - 3.938 + 3

     = -3.516 + 3

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3 0
2 years ago
Which property justifies the following statement?<br> If x = 2, and y = 3x - 11, then y = 3.2 - 11.
irina [24]

Answer:

Transitive property

But it looks like substitution.

Step-by-step explanation:

3 0
3 years ago
Can someone help me with part B? Thank you! Brainliest for correct answer!
Ivanshal [37]

Answer: The mean is 5

Step-by-step explanation:

If you add all of the numbers and divide by how much numbers there are (8), then you get 5. Then the mean absolute deviation is the number away from the mean.

So I will put the mean absolute deviation in order of the numbers

4 (1 away from mean), 3 (2 away from the mean), 4( 1 away from the mean), 5 (same number as the mean), 6 (1 away from the mean), 6(1 away from mean), 8 (3 away from mean), and, finally another 4 (1 away)

Hope this helps :)

3 0
2 years ago
Read 2 more answers
A line passes through the points (0, –3) and (2, –4) . What is the slope of the line?
Fudgin [204]
<span>(0, –3) (2, –4)
slope = difference in y divided by </span><span>difference in x
</span>
<span>slope = (-3 --4) / (0 -2) =
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</span>
3 0
3 years ago
Read 2 more answers
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Roman55 [17]

Answer: she still has to cut off 19/16 inches.

Step-by-step explanation:

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She has already cut off 2 9/16 inches from the piece of string. Converting 2 9/16 inches to improper fraction, it becomes 41/16 inches.

Therefore, the length of string that is left for her to cut off would be

15/4 - 41/16 = (60 - 41)/16

= 19/16 inches

6 0
3 years ago
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