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\[\lim_{n \rightarrow \infty}2n^2/n^2-2\]
Just take \[n^2\] common from denominator, \[\lim_{n \rightarrow \infty} 2n^2/n^2(1-2/n^2)\] Cancel whatver is being cancelled and then put the limit, \[\lim_{n \rightarrow \infty} 2/(1 - 2/n^2)\] Put the limit, Remember one thing:\[x/\infty = 0\] \[2/(1 - 2/\infty^2)\] \[2/(1 - 0)\] = 2 is the answer...
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