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question mark

The function f(x) = |2sgn(2x)| + 2 has
jump discontinuity
infinite discontinuity
removable discontinuity
no discontinuity at x=0

Drake , 11 Years ago
Grade 12
anser 1 Answers
Jitender Singh
Ans:
f(x) = |2sgn(x)| + 2
Left Hand Limit (LHL):
LHL = \lim_{x\rightarrow 0^{-}} (|2sgn(x)| + 2) = |2.(-1)| + 2 = 4
Right Hand Limit (RHL):
RHL = \lim_{x\rightarrow 0^{+}} (|2sgn(x)| + 2) = |2.(1)| + 2 = 4
f(0) = |2.(0)| + 2 = 2
LHL = RHL\neq f(0)
-> f(x)have finite removable discontinuity at x = 0
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty
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