If f(x) is continuous and f(92)=29, then _x0f(1-3xx^2) is equal to:

Question

If $f(x)$ is continuous and $f\left(\dfrac92ight)=\dfrac29$, then $\displaystyle\lim_{x	o0}f\left(\dfrac{1-\cos3x}{x^2}ight)$ is equal to:

Accepted Answer

$\displaystyle\lim_{x	o0}\frac{1-\cos3x}{x^2}=\frac{9}{2}$ (standard limit). By continuity, $\displaystyle\lim_{x	o0}f\left(\frac{1-\cos3x}{x^2}ight)=f\left(\frac92ight)=\frac29$.

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