What is \lim_{x\rightarrow 0-}h(x) equal to?
Consider the following for the next two (02) items that follow: Let f(x)=|x| and g(x)=[x]-1, where [.] is the greatest integer function. Let h(x)=\frac{f(g(x))}{g(f(x))}.
- A. -2 ✓
- B. -1
- C. 0
- D. 2
Correct Answer: A. -2
Explanation
As x \rightarrow 0-, x is a small negative number, so [x] = -1. Then g(x) = -1 - 1 = -2, and f(g(x)) = |-2| = 2. Also, f(x) = |x| = -x (which is a small positive number), so g(f(x)) = [-x] - 1 = 0 - 1 = -1. Thus h(x) = \frac{2}{-1} = -2.
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