Dear Baha,

AS limit x-> 0+

mod(x+1) is always positive

and mod(x-1) = (1-x) because for a small nighobur hood in 0+ the value of x-1 comes out to be negative

Hence for limit x->0+

hte functions is =  (x+1-(1-x))/x = 2

As limit x->0-

mod(x+1) is always positive for a samll neighbour hood in 0- x+1 is alwyas positive

mod(x-1) is = -(x-1)

Hence for limit x->0-

((x+1)- (-(x-1))) /x = 2

Hence the answer is 2

Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.

All the best.

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