Find `lim_(x to 0) f(x)`, where `f(x) = {{:(x -1,x lt 0),(0,x = 0),(x =1,x gt 0):}`

Explanation

Firstly, we evaluate f(x), when `x lt 0` for that we need to evaluate x - 1
`{:(x,-0.1,-0.01,-0.001,-0.0001),(f(x) = x - 1,-1.1,-1.01,-1.101,-1.0001):}`
Now, we evaluate f(x) for `x gt 0`, for that we need to evaluate x + 1
`{:(x,0.0001,0.001,0.01,0.1),(f(x) = x + 1,1.0001,1.001,1.01,1.1):}`
From the first table, we observe that value of the function is decreasing to -1 and hence `underset(x to 0)(lim) f(x) = 1`
From the second table, we observe that value of the function is increasing from 1 and hence `underset(x to 0^(+))(lim) f(x) = 1`
Since the left and right hand limits at 0 do not coincide, we say that the limit of the function at 0 does not exist

Graph of this function is also shown here, we can see that the value of the function at x = 0 is well defined and is equal to 0, but the limit of the function at x = 0 is not even defined.