# Let's do some calculus! (31)

Calculus Level 4

$f(x) = \begin{cases} x+1 & x>0 \\ 2-x & x \le 0 \end{cases} \quad \quad g(x) = \begin{cases} x+3 & x<1 \\ x^2 - 2x - 2 & 1 \le x < 2 \\ x-5 & x \ge 2 \end{cases}$

Let $$f(x)$$ and $$g(x)$$ be functions satisfying the conditions above. Find $$\displaystyle \left| \lim_{x \to 0} \big(g \circ f(x)\big) \right|$$.

Notations:

• $$g \circ f(x)$$ denotes the function $$g~\text{of}~ f(x)$$ or $$g\big(f(x)\big)$$.
• $$| \cdot |$$ denotes the absolute value function.