Confusion.....Help....

why lim (n---->∞) 0 * n = 0.....
even when we know that 0 * ∞ is an indeterminate quantity......

plzzz xplain.....(sorry don't know how to write this in latex)

thanks in advance....

Note by Riya Gupta
5 years ago

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Agreeing with Bob K. Before applying the limit we need to get rid of indeterminate form hence \(0 \cdot n\) gives \(0\). Another way to think about is that limits with \(n \rightarrow \infty\) is limit of this sequence \(0 \cdot n_1+0 \cdot n_2 \ldots\) in this case. Obviously with each term zero, limit is also zero.

Nishanth Hegde - 5 years ago

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Because $\infty \cdot 0$ is indeterminate, we need to be able to simplify it in the limit. It simplifies to ${lim}_{n \rightarrow +\infty } 0$ which is of course zero. The whole idea of a limit is to sort of express an indeterminate quantity. So as n gets very large, zero times n is still zero. That's all that's saying.

Bob Krueger - 5 years ago

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thanks....guys...u cleared my this confusion...:)

Riya Gupta - 5 years ago

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\(\lim_{n \to +\infty} 0*n\)

Aditya Parson - 5 years ago

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Do you mean 0^∞ or 0 x ∞ ?

Bhargav Das - 5 years ago

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0 * ∞

Riya Gupta - 5 years ago

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