Q. 165.0( 2 Votes )

Find the values of a and b such that the function f defined by



is a continuous function at x = 4.

Answer :

Given,


…(1)


We need to find the value of a & b such that f(x) is continuous at x = 4.


A function f(x) is said to be continuous at x = c if,


Left hand limit(LHL at x = c) = Right hand limit(RHL at x = c) = f(c).


Mathematically we can represent it as-



Where h is a very small number very close to 0 (h0)


Now, let’s assume that f(x) is continuous at x = 4.



As we have to find a & b, so pick out a combination so that we get a or b in our equation.


In this question first we take LHL = f(4)



{using equation 1}



h > 0 as defined in theory above.


|-h| = h




a – 1 = a + b


b = -1


Now, taking other combination,


RHL = f(4)



{using equation 1}



h > 0 as defined in theory above.


|h| = h




b + 1 = a + b


a = 1


Hence,


a = 1 and b = -1


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