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

Question

(C) To find the limits at $x = 3$,we evaluate the left-hand limit and right-hand limit separately.For the right-hand limit $(x 	o 3^+)$,we use the de

Vedclass · Accepted Answer

$\lim_{x 	o 3^+} f(x) 
eq \lim_{x 	o 3^-} f(x)$

Vedclass · Answer

(C) To find the limits at $x = 3$,we evaluate the left-hand limit and right-hand limit separately.For the right-hand limit $(x 	o 3^+)$,we use the definition $f(x) = 5 - x$:$\lim_{x 	o 3^+} f(x) = 5 - 3 = 2$.For the left-hand limit $(x 	o 3^-)$,we use the definition $f(x) = \frac{2}{5-x}$:$\lim_{x 	o 3^-} f(x) = \frac{2}{5 - 3} = \frac{2}{2} = 1$.Since $2 
eq 1$,we have $\lim_{x 	o 3^+} f(x) 
eq \lim_{x 	o 3^-} f(x)$.

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

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