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Let f(x) = {(x "sin "(1)/(x)","," if " x...

Let `f(x) = {(x "sin "(1)/(x)","," if " x != 0),(" 0,"," where " x = 0):}`
Then, which of the following is the true statement ?

A

f(x) is not defined at x = 0

B

`underset(x rarr 0)(lim) f(x)` does not exist

C

f(x) is continuous at x = 0

D

`f(x)` is discontinuous at x = 0

Text Solution

Verified by Experts

The correct Answer is:
C
`f(0) = 0`
`underset(x rarr 0)(lim) f(x) = underset(x rarr 0)(lim) x "sin " (1)/(x) = 0 xx ("a finite quantity") = 0`
`:. f(x)` is continuous at `x = 0`
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