Question

Question 30 Suppose f(x) ={ |x| + 1, x < 0
4, x = 0
|x| - 1, x > 0 }
For what value(s) of a does lim(x-->a) f(x) exists?

Class XI - Limits and Derivatives Page 303

Answer 1

        {|x| +1 , x<0
f(x) ={ 4 , x = 0
        { |x| -1 , x> 0
here we see zero is the suspicious point.we should check limit value in point zero.
Lim(x→0⁻) (|x|+1) =1 
lim(x→0⁺)(|x|-1) = -1 
hence, limit doesn't  exist at x = 0 so, A value of a isn't zero.
except zero f(x) exist in everywhere. so, the values of a ∈ R -{0}