# Let . If f(x) is continuous at find a and b.  (CBSE 2016)

Given:

f(x) is continuous at x = & f( ) = a,

If f(x) to be continuous at x = ,we have to show, f( ) = f( ) + = f( )

LHL = f( ) =   sin( –x) = cosx cos( –x) = sinx    (a3–b3) = (a–b)(a2 + ab + b2)    cos(0) = 1   ...(1)

LHL = f( ) + =           1 ...(2)

f(x) is continuous at x = & f( ) = a ,and from (1) & (2),we get

f( ) = f( ) + = f( ) = a a =  b = 4

Hence ,a = & b = 4

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