The degree rule at infinity

You will write three functions that find the limit of a fraction of polynomials as $x \to \infty$ by comparing the degrees. A polynomial is stored as a list of coefficients, highest power first. For example [3, 5, 0] means $3x^2 + 5x$.

The idea. The degree is the highest power that has a non-zero coefficient. If the top has the lower degree, the limit is $0$. If the degrees are equal, the limit is the ratio of the leading coefficients. If the top has the higher degree, there is no finite limit.

Your tasks.

1. Finish degree(coeffs). Skip leading zeros, and return the highest power that has a non-zero coefficient.
2. Finish limit_at_infinity(top, bottom). Return the limit as a number, or the word "none" when there is no finite limit.
3. Finish value(coeffs, x). Return the value of the polynomial at x.