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.

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