If f(x) = begin{cases} frac{1}{x} sin(x^2), & | vedclass

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(C) To check the continuity of $f(x)$ at $x = 0$,we evaluate the limit as $x 	o 0$.Given $f(x) = \frac{\sin(x^2)}{x}$ for $x 
e 0$.We can rewrite th

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$f(x)$ is continuous at $x = 0$

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(C) To check the continuity of $f(x)$ at $x = 0$,we evaluate the limit as $x 	o 0$.Given $f(x) = \frac{\sin(x^2)}{x}$ for $x 
e 0$.We can rewrite this as $f(x) = x \cdot \frac{\sin(x^2)}{x^2}$.Now,$\lim_{x 	o 0} f(x) = \lim_{x 	o 0} \left( x \cdot \frac{\sin(x^2)}{x^2} ight)$.Since $\lim_{x 	o 0} \frac{\sin(x^2)}{x^2} = 1$ and $\lim_{x 	o 0} x = 0$,we have $\lim_{x 	o 0} f(x) = 0 \cdot 1 = 0$.Since $\lim_{x 	o 0} f(x) = f(0) = 0$,the function $f(x)$ is continuous at $x = 0$.

If $f(x) = \begin{cases} \frac{1}{x} \sin(x^2), & x \ne 0 \\ 0, & x = 0 \end{cases}$,then

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