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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

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

Grade:12

2 Answers

Dhruv Sunil Agarwal
36 Points
9 years ago

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

nikhil arora
54 Points
9 years ago

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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