F(x) = cases 1 - 4x x^2 &

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

f(x)={1−cos⁡4xx2,x<0a,x=0x16+x−4,x>0f(x) = \begin{cases} \frac{1 - \cos 4x}{x^2} & , x < 0 \\ a & , x = 0 \\ \frac{\sqrt{x}}{\sqrt{16 + \sqrt{x}} - 4} & , x > 0 \end{cases} If f(x)f(x) is continuous at x=0x = 0, find the value of aa.

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