Evaluate the following limit.

Question

lim x + 1 / | x + 1|

x→-1

Answer 1

When x < -1, x+1 is negative So l x+1 l = -(x+1)

When x > -1, x+1 is positive. So, l x+1 l = x+1

Taking one-sided limits, you will see that they are not the same. Therefore, the given limit does not exist (DNE)

Answer 2