Question

What is the values of' 'k' so that the function 'f' is continuous at the indicated point

Options

• 4

• 6

• 8

• 10

Answer 1

6

Explanation:

L.H.L = `lim_(h -> pi/2) (k cos x)/(pi - 2x)`, putting `x = pi/2 - h`

= `lim_(h -> 0) (k cos (pi/2 - h))/(pi - 2(pi/2 - h))`

= `lim_(x -> (pi^+)/2) (k cos x)/(pi - 2x)`,

R.H.L = `lim_(x -> (pi^+)/2) (k cos x)/(pi - 2x)`, putting `x = pi/2 + h`

= `k cos  ((pi/2 + h))/(pi - 2(pi/2 + h))`

= `lim_(h -> 0) (- k sin h)/(-2 h)`

= `lim_(h -> 0) k/2 sinh/h = k/2`

`f(pi/2)` = 3  ......[Given]

`f` is continuous, if `k/2` = 3 or k = 6.