Sequencing Genome, I mean Limits

Calculus Level 3

Let \(a = \min (x^2+2x+3) \) and \(b = \displaystyle \lim_{x \to 0} \frac { \sin x \ \cos x}{e^x - e^{-x} } \) for real parameter \(x\).

What is the value of \( \displaystyle \sum_{r=0}^n a^r b^{n-r} \)?


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