# Think innovatively

Geometry Level 5

Let $f(x)= 1+3x^2 + 5x^4 + 7x^6+ \cdots + 21x^{20} , \quad x \in \mathbb{R}$

and $g(x) = -x^2 + 4 \cos^2b- 4 \sin b -7, \quad b \in \mathbb{R}$

If $$d$$ is the shortest distance between $$f(x)$$ and $$g(x)$$ and $$d_1,d_2$$ are the greatest and least values of $$d$$ respectively, then $$\dfrac {d_1}{d_2}=?$$

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