For a ∈ N , define f ( 1 ) = b and f ( x ) = x − 1 ( 7 + x 3 ) 1/ a − ( 3 + x 2 ) 1/2 for x  = 1 . If f is continuous at 1 , find a + 4 b .

Question

For a ∈ N , define f ( 1 ) = b and f ( x ) = x − 1 ( 7 + x 3 ) 1/ a − ( 3 + x 2 ) 1/2 ​ for x  = 1 . If f is continuous at 1 , find a + 4 b .

TestHub · Accepted Answer

A finite limit requires 8 1/ a = 4 1/2 = 2 , hence a = 3 . Differentiating the numerator at 1 gives b = 1/4 − 1/2 = − 1/4 . Therefore a + 4 b = 3 − 1 = 2 .

Mathematics - Continuity - Differentiability Question with Solution | TestHub

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