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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
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