Basic Limits

Calculus Level 3

\[\large f(x) = x^{5a+1}\]

Function \(f(x)\) is defined as above, where \(\displaystyle a = \lim_{n \to -2} \frac {2(n^3-2n+4)}{n^3+3n^2+n-2} \).

If \(\dfrac {d^{100}f(x)}{dx^{100}} = y!\) at \(x=1\), find \(y\).

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