What is \lim_{x\rightarrow0}\{f(x)g(x)\} equal to?
Consider the following for the two (02) items that follow : Let the function f(x)=\sin[x], where [x] is the greatest integer function and g(x)=|x|.
- A. -1
- B. 0 ✓
- C. 1
- D. Limit does not exist
Correct Answer: B. 0
Explanation
As x \to 0, g(x) = |x| \to 0. The function f(x) = \sin[x] is bounded since -1 \leq \sin[x] \leq 1. By the Squeeze Theorem, \lim_{x \to 0} f(x)g(x) = 0.
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