MathDB

Let

a_0, a_1,\dots, a_{19} \in \mathbb{R}

and

P(x) = x^{20} + \sum_{i=0}^{19}a_ix^i, x \in \mathbb{R}.

P(x)=P(-x)

for all

x \in \mathbb{R}

, and

P(k)=k^2,

for

k=0, 1, 2, \dots, 9

then find

\lim_{x\rightarrow 0} \frac{P(x)}{\sin^2x}.

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