Question

Find the value of k if f(x) is continuous at x = π/2, where f(x)
k cos x/π-2x , x ≠ π/2
3 , x = π/2​

Answer 1

The function f is continuous at x = pie/2

x= pie/2 f(x) = f (pie/2)

x= pie/2 k cosx / pie-2x =3

since x= pie/2 put x= pie/2+h

As x=pie/2 , h=0

substituting the value of x as pie/2+h

in above equation , we get

h=0 Kcos[pie/2+h] ÷ pie-2 [pie/2+h] = 3

h=0 k(-sin h ) ÷ -2h = 3

k/2 h=0 sin h÷ h = 3

k/2 ×1 = 3

k/2 = 3

therefore k = 6 .

Here is your answer