Question: 1. Let m be a fixed natural number, and suppose that Pm is a polynomial with rational coefficients (in other words, Pm(z) = E,

1. Let m be a fixed natural number, and suppose that Pm is a polynomial with rational coefficients (in other words, Pm(z) = E, a4r', where a,, 0 Sism, are rational numbers). Prove that either %3D 2" = 0 0 ePm(n) lim %3D or em (n) lim = 0. 2n 2. Evaluate the following limit: lim z-0 2 sin? du.

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