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For the function f(x)={((x^(3)-a^(3))/(...

For the function `f(x)={((x^(3)-a^(3))/(x-a)",",x ne a),(b" ,",x =a):}`, if f(x) is continuous at x = a, then b is equal to

A

`a^(2)`

B

`2a^(2)`

C

`3a^(2)`

D

`4a^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`LHL= lim_(x to a^(-)) (x^(3)-a^(3))/(x-a)=lim_(hto0) ((a-h)^(3)-a^(3))/(a-h-a)`
`=lim_(h to 0) ((a-h-a){(a-h)^(2)+a^(2)+a(a-h)})/(-h)=3a^(2)`
Since, f(x) is continuous at x = a.
`therefore LHL=f(a) rArr 3a^(2)=b`
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