For the function f(x) = begin{cases} frac{sin | vedclass

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(B) To check the continuity of $f(x)$ at $x = 0$,we evaluate the limit: $\lim_{x 	o 0} f(x) = \lim_{x 	o 0} \frac{\sin^2(ax)}{x^2} = \lim_{x 	o 0}

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$f(x)$ is discontinuous at $x = 0$,when $a 
eq \pm 1$

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(B) To check the continuity of $f(x)$ at $x = 0$,we evaluate the limit: $\lim_{x 	o 0} f(x) = \lim_{x 	o 0} \frac{\sin^2(ax)}{x^2} = \lim_{x 	o 0} \left( \frac{\sin(ax)}{ax} ight)^2 \cdot a^2 = (1)^2 \cdot a^2 = a^2$. The value of the function at $x = 0$ is $f(0) = 1$. For $f(x)$ to be continuous at $x = 0$,we must have $\lim_{x 	o 0} f(x) = f(0)$,which implies $a^2 = 1$,or $a = \pm 1$. If $a 
eq \pm 1$,then $a^2 
eq 1$,so $\lim_{x 	o 0} f(x) 
eq f(0)$. Thus,$f(x)$ is discontinuous at $x = 0$ when $a 
eq \pm 1$.

For the function $f(x) = \begin{cases} \frac{\sin^2(ax)}{x^2}, & x \neq 0 \\ 1, & x = 0 \end{cases}$,which one is a true statement?

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