# Basic Limits

Calculus Level 3

Let a function f(x) be defined as: $$f(x) = x^{5a+1}$$, where a is:

$$a = \underset { n\rightarrow -2 }{ lim } \frac { 2({ n }^{ 3 }-2n+4) }{ { n }^{ 3 }+{ 3n }^{ 2 }+n-2 }$$

then $$\frac { { d }^{ 100 }(f(x)) }{ d{ x }^{ 100 } } =\quad y!$$ at x = 1.

Find y.

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