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If a in I, then value of a for which lim...

If `a in I`, then value of a for which `lim_(xrarra) (tan([x^(2)]-[x]^(3)))/((x-a)^(3))` exists finitely, is /are

A

0

B

1

C

`-1`

D

2

Text Solution

Verified by Experts

The correct Answer is:
A, B
Let `f(x)={x^(3)}-{x}^(3)`
`f(a)=0`
`(a^(+))=a^(3)-a^(3)=0`
`f(a^(-))=underset(hrarr0)(lim)([(a-h)^(3)]-[a-h]^(3))=a^(3)-1-(a-1)^(3)=3a(a-1)`
Since `f(a^(-))=0 rArr 3a(a-1)=0 rArr a=0 or a=1`
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