the function f(x)= sin(ln mod(x)), x not equal to 0 and 1

if x=0:

a) is continuous at x=0

b) has removable discontinuity at x=0

c) has jump discontinuity at x=0

d) has oscillating discontinuity at x=0

We have lim x tends to 0^- f(x)=lim h tends to 0 sin(ln l-hl )= lim h tends to 0 sin (ln h )

which does not exist but lies between -1 and 1.

Similarly, lim x tendsto 0^+ f(x) lies between -1 and 1 but cannot be determined.

Therefore answer is d)

in above solution 0^- and 0^+ means 0 minus and 0 plus

The answer shud be D. 

putting x=0 in f(x) ,

f(0) = sin (ln(0)) = sin(-∞) which is an oscillating value between -1 and 1