Question

Does the limit (Lim x →0 |x|/x) exist?

Answer 1

limit doesn't exist.done

Answer 2

Hey there !!!!!

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Limit of a function exists when RHL(Right hand limit)=LHL(Left hand limit)

When x tends to 0⁺  x is positive and when x tends to 0⁻ "x" is negative

So Right hand limit :

Limlxl/x= x/x=1
ˣ⁻⁰⁺

Left hand limit:

limlxl/x=x/-x= -1
ˣ⁻⁰⁻

Left hand limit is not equal to right hand limit 

So, limlxl/x is discontinuous .
      ˣ⁻⁰

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Hope this helped you.........