Given,

…(1)

We need to find the value of k such that f(x) is continuous at x = 2.

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 (h→0)

Now, let’s assume that f(x) is continuous at x = 2.

∴

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(5)

∴

⇒ {using equation 1}

⇒

⇒

⇒

As the limit can’t be evaluated directly as it is taking 0/0 form.

So, use the formula:

Divide the numerator and denominator by -h to match with the form in formula-

Using algebra of limits, we get,

k =

∴ k =