Evaluate \displaystyle\lim{h\to 0}\dfrac{(3+h)^2 - 9}{h}.

6 (3+h)^2 - 9 = 6h + h^2. Divide by h: 6 + h \to 6. (This is f'(3) for f(x) = x^2.)

Defining the Derivative and Using Derivative Notation

AP Calculus AB· difficulty 3/5

\displaystyle\lim_{h\to 0}\dfrac{(3+h)^2 - 9}{h}

Explanation

(3+h)^2 - 9 = 6h + h^2

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