Evaluate \displaystyle\lim{x\to 0}\dfrac{(x+2)^2 - 4}{x}.

4 Expand: (x+2)^2 - 4 = x^2 + 4x + 4 - 4 = x^2 + 4x. Divide by x: x + 4 \to 4.

Determining Limits Using Algebraic Manipulation

AP Calculus AB· difficulty 3/5

\displaystyle\lim_{x\to 0}\dfrac{(x+2)^2 - 4}{x}

Explanation

(x+2)^2 - 4 = x^2 + 4x + 4 - 4 = x^2 + 4x

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