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. 1
Correct Answer: B. -1
Explanation
As x \rightarrow 0+, x is a small positive number, so [x] = 0. Then g(x) = 0 - 1 = -1, and f(g(x)) = |-1| = 1. Also, f(x) = |x| = x, so g(f(x)) = [x] - 1 = 0 - 1 = -1. Thus h(x) = \frac{1}{-1} = -1.
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