If the function f(x), defined below is continuous at x = 0, find the value of k:

we have to find the value of 'k'

Given:

f(x) is continuous at x = 0 & f(0) = k

If f(x) is be continuous at x = 0,then,

f(0)^–=f(0) ⁺ = f(0)

LHL = f(0)^– =

cos(0) = 1

⇒ (1)²

⇒ 1

RHL = f(0) ^{+ =}

⇒ 1

Since , f(x) is continuous at x = 0 & f(0) = k

And also , f(0)^– ₌ f(0) ⁺ ₌ f(0)

So ,k = 1