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At x=3, f(x) ={(x^(5)-243",", "if " x ne...

At `x=3, f(x) ={(x^(5)-243",", "if " x ne 3),(x^(3)-27",", "if " x=3):}` is

A

continuous

B

discontinuous

C

underfined

D

removable discontinuous

Text Solution

Verified by Experts

The correct Answer is:
A
Given , `f(x)={ (x^(5)-243",", " if " x ne 3), (x^(3)-27"," , "if " x =3):}`
Now `LHL=lim_(x to 3^(-)) f(x)=lim_(x to a)(x^(5)-243)`
`=(3)^(5) -243 =0`
`RHL = lim_(x to 3^(+)) f(x) =lim_(x to a) (x^(5)-243)`
`=(3)^(5) -243=0`
`and f(3)=3^(3) -27=0`
`therefore LHL=RHL=f(3)`
Hence, f(x) is continuous at x = 3.
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-CONTINUITY-EXERCISE 2 (MISCELLANEOUS PROBLEMS)
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