If f(x)=\frac{x^{2}+x+|x|}{x}, then what is \lim_{x\rightarrow0}f(x) equal to ?
- A. 0
- B. 1
- C. 2
- D. \lim_{x\rightarrow0}f(x) does <strong>NOT</strong> exist ✓
Correct Answer: D. \lim_{x\rightarrow0}f(x) does <strong>NOT</strong> exist
Explanation
For x \gt 0, |x|=x, so f(x) = \frac{x^2+2x}{x} = x+2, giving a Right Hand Limit (RHL) of 2. For x \lt 0, |x|=-x, so f(x) = \frac{x^2}{x} = x, giving a Left Hand Limit (LHL) of 0. Since LHL \neq RHL, the limit does not exist.
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