What is \lim_{x\rightarrow0}f^{\prime}(x) equal to?
Consider the following for the two (02) items that follow : Let f(x)=\begin{cases}x^{3},&x^{2}\lt 1\\ x^{2},&x^{2}\geq 1\end{cases}
- A. 2
- B. 1
- C. 0 ✓
- D. Limit does not exist
Correct Answer: C. 0
Explanation
In the neighborhood of x=0, x^2 \lt 1, so the function is defined as f(x) = x^3. Its derivative is f'(x) = 3x^2. The limit as x \to 0 is \lim_{x\rightarrow0} 3x^2 = 0.
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