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matrenka [14]
3 years ago
10

Evaluate the limit 12n^3 - 2n^2 + 9 / 4n^3

Mathematics
1 answer:
geniusboy [140]3 years ago
7 0

Answer:

3

Step-by-step explanation:

Evaluate the limit n - > ∞ 12n^3 - 2n^2 + 9 / 4n^3

Divide the expression by the highest power of n to have

limit n - > ∞ 12n³/n³ - 2n²/n³ + 9/n³ / 4n³/n³

= limit n -  > ∞12 - 2/n + 9/n³ / 4

Substitute the value of n

= 12 - 2/∞ + 9/∞³ / 4

Since a/∞ = 0

The expression becomes;

= 12 - 0+ 0/4

= 12/4

= 3

Hence the required limit is 3

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The sum of three consecutive integers is -234 find the integers​
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Answer:

-77, -78, -79

Step-by-step explanation:

let one of the integers be x

since the integers are consecutive, the other 2 integers must be

(x+1) and (x+2)

given that sum of the integers is -234,

x + (x+1) + (x+2) = -234

x + x + 1 + x + 2 = -234

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3x = -234-3

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x = -237 / 3

x = -79  (answer)

hence the other two numbers are

(x + 1) = -79 + 1 = -78 (answer)

and

(x+2) = -79 + 2 = -77 (answer)

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docker41 [41]

Answer:

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Step-by-step explanation:

We have to simplify these ratios.

If the most simplified form of the ratios are equal, they are equivalent

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24:54

r = \frac{24}{54} = \frac{12}{27} = \frac{4}{9}

18:54

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The ratio will be same

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