Break the limit at x = 1,
i.e calculate LHL and RHL and then see, if they come out to be unequal, then limit doesn’t exist, else limit exist.
Now, for LHL, |x – 1|, if x < 1 then it become -(x – 1)
so, LHL = lim h→0 ((1-h)^16 – 1) / (-(1-h – 1)), on calculating it comes out to be -17(please do a check)
similarily RHL = lim h→0 ((1+h)^16 – 1) / (1+h-1), which comes out to be 15(calculation might be wrong)
clearly, limit doesn’t exist at x = 1.
Option D