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3241004551 [841]
3 years ago
7

If n is a positive integer, then lim (n-->infinity) (1/n) [1/(1+(1/n)) + 1/(1+(2/n))+...+1/(1+(n/n)] is?

Mathematics
1 answer:
Anton [14]3 years ago
3 0
The correct answer to this question is <span>d.) integral from 1 to 2 of (2/(x+1))
</span>To solve this:

Since Δx = 1/n. 
lim (n→∞) Δx [1/(1+Δx) + 1/(1+2Δx)+ ... + 1/(1+nΔx)] 
= lim (n→∞) Σ(k = 1 to n) [1/(1 + kΔx)] Δx. 

x <---> a + kΔx 

a = 0, then b = 1, so that Δx = (b - a)/n = 1/n

Since (1 + kΔx) combination, a = 1 so that b = 2. 
Then, f(1 + kΔx) <-----> f(x) ==> f(x) = 1/x. 

This sum represents the integral 
∫(x = 1 to 2) (1/x) dx, so the correct answer is <span>d.) integral from 1 to 2 of (2/(x+1))

Thank you for posting your question. I hope that this answer helped you. Let me know if you need more help. 
</span>
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9514 1404 393

Answer:

  √145 ≈ 12.04

Step-by-step explanation:

The length of the space diagonal is the root of the sum of the squares of the prism edge lengths:

  d² = a² +b² +c² = 6² +3² +10² = 145

  d = √145 ≈ 12.04 . . . inches

__

The face diagonal is found using the Pythagorean theorem in the usual way:

  f² = a² + b²

The space diagonal is the hypotenuse of the right triangle whose sides are the face diagonal and the remaining edge:

  d² = f² +c²

  d² = a² +b² +c²

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Here is a diagram.

3 0
3 years ago
4. Solve for w:<br> -33 = 6 - 3w
gavmur [86]

Answer:

13 =w

Step-by-step explanation:

-33 = 6 - 3w

Subtract 6 from each side

-33-6 = 6 - 3w-6

-39 = -3w

Divide each side by -3

-39/-3 = -3w/-3

13 =w

3 0
3 years ago
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Suppose that a certain movie earns $3,000,000 in ticket sales. If 60% goes to the movie and 40% goes to theatres: Movie studios
miskamm [114]

Answer: See explanation

Step-by-step explanation:

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Percentage that went to movie = 60%

Percentage that went to theater = 40%

Revenue gotten by movie studio = 60% × $3,000,000

= 0.6 × $3,000,000

= $1,800,000

Revenue gotten by theaters = 40% × $3,000,000

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= $1,200,000

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Answer:

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Step-by-step explanation:

If this is the system of equations here is how:

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