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Solve lim(x->5) [x-5/|x-5|]

Solve
lim(x->5) [x-5/|x-5|]

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

L = \lim_{x\rightarrow 5}\frac{x-5}{|x-5|}
L_{1} = \lim_{x\rightarrow 5^{-}}\frac{x-5}{|x-5|}
L_{1} = \lim_{x\rightarrow 5^{-}}\frac{x-5}{-(x-5)}
L_{1} = -1
L_{2} = \lim_{x\rightarrow 5^{+}}\frac{x-5}{|x-5|}
L_{2} = \lim_{x\rightarrow 5^{+}}\frac{x-5}{(x-5)}
L_{2} =1
So right hand and left hand limits are different.
Limit does not exist.

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