# 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 $$y$$.

×