If f(x) = begin{cases} frac{sin x}{x} + cos x | vedclass

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(C) To check the continuity at $x = 0$,we evaluate the left-hand limit,right-hand limit,and the value of the function at $x = 0$.$1$. Right-hand limit

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

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(C) To check the continuity at $x = 0$,we evaluate the left-hand limit,right-hand limit,and the value of the function at $x = 0$.$1$. Right-hand limit: $\lim_{x 	o 0^+} f(x) = \lim_{x 	o 0^+} (\frac{\sin x}{x} + \cos x) = 1 + 1 = 2$.$2$. Left-hand limit: $\lim_{x 	o 0^-} f(x) = \lim_{x 	o 0^-} (\frac{\sin x}{x} + \cos x) = 1 + 1 = 2$.$3$. Value of the function: $f(0) = 2$.Since $\lim_{x 	o 0^+} f(x) = \lim_{x 	o 0^-} f(x) = f(0) = 2$,the function $f(x)$ is continuous at $x = 0$.

If $f(x) = \begin{cases} \frac{\sin x}{x} + \cos x, & x \ne 0 \\ 2, & x = 0 \end{cases}$,then which of the following is true?

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