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3. Lim
x-infinity
x² +6x²+1/
x²+3
[AP]

3. Lim x-infinity x² +6x²+1/ x²+3 [AP]-example-1
User Sallf
by
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1 Answer

2 votes

Answer: 0

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Step-by-step explanation:

Let n be the degree of the numerator

Let d be the degree of the denominator

If n < d, then the limit at infinity is always 0. This is because the denominator is growing faster compared to the numerator. I suggest looking at a table of values to see this in action.

In this case, n = 3 and d = 4, so we see that n < d is the case here. So that's why the answer is 0.

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Side notes:

  • If n = d, then the limit at infinity is equal to a/b, where a and b are the leading terms of the numerator and denominator.
  • If n > d, then the numerator is growing faster than the denominator, meaning the ultimate result is infinity.
User Arunbh Yashaswi
by
5.8k points