Question

The limit of the function defined by `f(x) = {{:(|x|/x",", if x ≠ 0),(0",", "otherwisw"):}`

Options

• Exists and equals 1

• Exists and equals – 1

• Doesn't exist

• None of the above

Answer 1

Doesn't exist

Explanation:

Here `lim_(x -> 0^-)  f(x) = - 1 and f(0) = 0`

`lim_(x -> 0^+) f(x) = 1 ⇒ lim_(x -> 0^-) f(x) ≠ lim_(x -> 0^+) f(x)`