We have been given an integral $\int\limits^\infty _1 {\frac{1}{x^{0.999}} \, dx$ . We are asked to determine whether the given integral diverges or converges.

$\int _1^{\infty }\:\:\:\frac{1}{x^{0.999}}\:\:\:dx$

$\int _1^{\infty }\:\:\:\frac{1}{x^{0.999}}\:\:\:dx=\int _1^{\infty }\:\:\:x^{-0.999}\:\:\:dx$

$\int _1^{\infty }\:\:\:x^{-0.999}\:\:\:dx=\frac{x^{-0.999+1}}{-0.999+1}$

$\int _1^{\infty }\:\:\:x^{-0.999}\:\:\:dx=\frac{x^{0.001}}{0.001}$

$\int _1^{\infty }\:\:\:x^{-0.999}\:\:\:dx=1000x^{0.001}$

Let us compute the boundaries.

$1000(\infty)^{0.001}=\infty$

$1000(1)^{0.001}=1000$

Since $\infty-1000$ is not a finite number, therefore, the given integral diverges.

4 0

3 years ago

Identify the property 65 • 92 • 17 = 92 • 17 • ×

Mars2501 [29]

answer is 65

solving

65x92x17=92x17x

65=x

x=65

6 0

3 years ago

Cafe A offers 2 free bottled waters or juices for every 20 purchased.Cafe B offers 3 bottled waters or juices for every 25 purch

Dafna11 [192]

2/20

3/20

4 beverages for cafe A and 6 at cafe B

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3 years ago

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Write the expanded form of the expression.<br> y(0.75 + 7)<br> +

gregori [183]

Answer:

y(0.75+7) = 0.75y + 7y

Step-by-step explanation:

....

6 0

3 years ago

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