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Given f(x)={3-[cot^(-1)((2x^3-3)/(x^2))]...

Given `f(x)={3-[cot^(-1)((2x^3-3)/(x^2))] for x >0 and {x^2}cos(e^(1/x)) for x<0` (where {} and [] denotes the fractional part and the integral part functions respectively). Then which of the following statements do/does not hold good?

A

`f(0^(-))=0`

B

`f(0^(+))=3`

C

If `f(0)=0,` then f(x) is continuous at x = 0

D

Irremovable discontinuity of f at x = 0

Text Solution

Verified by Experts

The correct Answer is:
B, D
`underset(xrarr0^(+))(lim)(3-[cot^(-1)((2x^(3)-3)/(x^(2)))])=3-[cot^(-1)(-oo)]=0`
`underset(xrarr0^(-))(lim){x^(2)}cos(e^(1//x))=0xx"(value between -1 and 1)"`
`=0`
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