# Evil Limiting Function

Calculus Level 4

Suppose we define $$f(x) = \text{sgn}(\sin(x)) + \{ x\}$$ for $$2\leq x\leq4$$ and $$g(x) = -2 +|x-3|$$, find the value of $$\displaystyle \lim_{x\to3} g\circ f(x)$$.

Notations

• $$\text{sgn}(x)$$ denotes the signum function of $$x$$, $$\text{sgn}(x) = \begin{cases} 1 \quad,\quad x>0 \\ 0 \quad,\quad x=0 \\ -1 \quad,\quad x<0 \end{cases}$$.

• $$\{ x\}$$ denote the fractional part of $$x$$, $$\{x\} = x - \lfloor x\rfloor$$.

• $$g\circ f(x) = g(f(x))$$.

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