Exercise · ZW-DERIVATIVE-014 · ★☆☆ Basic
Interpret \(\displaystyle\lim_{x\to2}\frac{x^3-8}{x-2}\) as a derivative and compute it.
Choose one option.
Show answer
- B. \(12\)
Explanation
It is \(f'(2)\) for \(f(x)=x^3\), since \(f(2)=8\). As \(x^3-8=(x-2)(x^2+2x+4)\), the limit is \(4+4+4=12\).
Review the concept: Derivative
The derivative of \(f\) at \(a\) is the limit of the difference quotient as \(h\to0\). It measures the instantaneous rate of change and is the slope of the tangent line at \((a,f(a))\).
\[f'(a)=\lim_{h\to0}\frac{f(a+h)-f(a)}{h}\]
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