Question

Question 25 Evaluate lim(x-->0) f(x), where f(x) ={ |x| / x, x ≠ 0
0, x = 0 }

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→0-) f(x)
= lim x→0 -x/x
=> -1

right hand limit
lim(x→0+) f(x)
= lim(x→0) x/x
=> 1

so here LHL ≠ RHL
hence limit doesn't exists.