Question

For what value of `k` the following function is continuous at the indicated point

`f(x) = {{:(kx + 1",", if x ≤ pi),(cos x",", if x > pi):}` at = `pi`

Options

• `pi`

• `2/pi`

• `(-2)/pi`

• `2pi`

Answer 1

`(-2)/pi`

Explanation:

At `x = pi`,

L.H.L = `lim_(x -> pi) f(x) = lim_(x -> pi) - (kx + 1) = kpi + 1`

`f(x) = kpi + 1`

R.H.L = `lim_(x -> pi) cos x = -1`

For continuity at `x = pi`,

L.H.S = R.H.S = `f(pi)`

∴ `kpi + 1` = – 1

⇒ `k = (-2)/pi`