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)

Note by Riya Gupta
5 years, 4 months 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.

- 5 years, 4 months ago

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.

- 5 years, 4 months ago

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

- 5 years, 4 months ago

$$\lim_{n \to +\infty} 0*n$$

- 5 years, 4 months ago

Do you mean 0^∞ or 0 x ∞ ?

- 5 years, 4 months ago

0 * ∞

- 5 years, 4 months ago