Q. 135.0( 1 Vote )

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

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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