Question

Question 24 Find lim(x-->1) f(x), where f(x) = { x^2 - 1, x ≤ 1
-x^2 - 1, x > 1 }

Class XI - Limits and Derivatives Page 302

Answer 1

we know limit only exists when
Left hand limit = Right hand limit

so here left hand Limit =
lim(x→1-) f(x)
= lim(x→1) x²-1
=> 1-1 = 0

now right hand limit
lim(x→1+)f(x)
= lim(x→1) -x²-1
=> -1-1 = -2
so LHL ≠ RHS
hence limit doesn't exists.