Q. 135.0( 1 Vote )

Find the value of k so that the function f is continuous at the indicated point:

Answer :

Given,


…(1)


We need to find the value of k such that f(x) is continuous at x = 0.


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 = 0.



As we have to find k so pick out a combination so that we get k in our equation.


In this question we take LHL = f(0)



{using eqn 1}


-1


As we can’t find the limit directly because it is taking 0/0 form.


So, we will rationalize it.


-1


Using (a+b)(a-b) = a2 – b2 , we have –


-1


-1


-1


= -1


2k/2 = -1


k = -1


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