Find the limit of the sequence #ln(n^2+2) 1/2ln(n^4+4)#. Does it converge to 0?
Hence:
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To find the limit of the sequence ( \ln(n^2+2)  \frac{1}{2}\ln(n^4+4) ) as ( n ) approaches infinity, we'll analyze each term separately and then subtract them.

( \lim_{n \to \infty} \ln(n^2+2) = \infty ) because the natural logarithm function grows without bound as its argument approaches infinity.

( \lim_{n \to \infty} \frac{1}{2}\ln(n^4+4) = \infty ) because the natural logarithm function grows without bound as its argument approaches infinity.
Therefore, the difference ( \ln(n^2+2)  \frac{1}{2}\ln(n^4+4) ) also approaches infinity as ( n ) approaches infinity. It does not converge to 0.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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