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Question

Question: If \(f(x) = \left\{ \begin{matrix} \frac{2}{5 - x},\text{when}x < 3 \\ 5 - x,\text{when}x > 3 \end{m...

If f(x)={25x,whenx<35x,whenx>3 f(x) = \left\{ \begin{matrix} \frac{2}{5 - x},\text{when}x < 3 \\ 5 - x,\text{when}x > 3 \end{matrix} \right.\ , then

A

limx3+f(x)=0\lim_{x \rightarrow 3^{+}}f(x) = 0

B

limx3f(x)=0\lim_{x \rightarrow 3^{-}}f(x) = 0

C

limx3+f(x)limx3f(x)\lim_{x \rightarrow 3^{+}}f(x) \neq ⥂ \lim_{x \rightarrow 3^{-}}f(x)

D

None of these

Answer

limx3+f(x)limx3f(x)\lim_{x \rightarrow 3^{+}}f(x) \neq ⥂ \lim_{x \rightarrow 3^{-}}f(x)

Explanation

Solution

limx3+f(x)=53=2\lim_{x \rightarrow 3 +}f(x) = 5 - 3 = 2 and limx3f(x)=253=1\lim_{x \rightarrow 3 -}f(x) = \frac{2}{5 - 3} = 1