If f(x) = begin{cases} frac{5}{2} - x, & x

Question

(B) To check the continuity at $x = 2$,we evaluate the left-hand limit,right-hand limit,and the value of the function at $x = 2$.$1$. Left-hand limit:

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$f(x)$ is discontinuous at $x = 2$

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(B) To check the continuity at $x = 2$,we evaluate the left-hand limit,right-hand limit,and the value of the function at $x = 2$.$1$. Left-hand limit: $\lim_{x 	o 2^-} f(x) = \lim_{x 	o 2^-} (\frac{5}{2} - x) = \frac{5}{2} - 2 = \frac{1}{2}$.$2$. Right-hand limit: $\lim_{x 	o 2^+} f(x) = \lim_{x 	o 2^+} (x - \frac{3}{2}) = 2 - \frac{3}{2} = \frac{1}{2}$.$3$. Value of the function: $f(2) = 1$.Since $\lim_{x 	o 2^-} f(x) = \lim_{x 	o 2^+} f(x) = \frac{1}{2}$,the limit $\lim_{x 	o 2} f(x)$ exists and is equal to $\frac{1}{2}$.However,$\lim_{x 	o 2} f(x) 
eq f(2)$ because $\frac{1}{2} 
eq 1$.Therefore,$f(x)$ is discontinuous at $x = 2$.

If $f(x) = \begin{cases} \frac{5}{2} - x, & x < 2 \\ 1, & x = 2 \\ x - \frac{3}{2}, & x > 2 \end{cases}$,then:

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