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Algebra Level 4

$P(k)=2^k~\forall~0\leq k\leq 2015~\land~k\in\Bbb{Z}$

Consider a polynomial $P(x)$ of degree $2015$ which satisfies the condition above.

Let $s=\log_2\bigg(P(2016)\bigg)$ .

Then, which of the given options best describes the value of $s$ ?

s < 2016

s > 2016

s=2017

s=2016

1 solution

Eddie Zahr
Apr 25, 2015

I'm not sure this is a good example of left continuity... Seems a bit like an abuse of notation?

By $x\to a^-$ , I'm implying that $x=a-\delta$ such that $\delta\to 0^+$ , i.e., $\delta$ is a very small positive real. I don't think it counts as abuse of notation.

Then again, I may be wrong. You should post this as a report using the "Report Problem" option so that the mods can review if there is anything wrong with it.

Prasun Biswas - 6 years, 1 month ago

It is an abuse of notation. That is not what $x \rightarrow a^-$ means at all. $s$ is a fixed value, not a variable. It does not tend to 2016 on the negative side.

I have updated the answer to $s < 2016$ instead.

Calvin Lin Staff - 6 years, 1 month ago

Ah, well, that works! Thanks.

Prasun Biswas - 6 years, 1 month ago

Twice the fun

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