Question

Kcosx/pi-2x when xis nt equal to pi/2
3 if x=pi/2 find k

Answer 1

The value of k for the given function is 6  

Step-by-step explanation:

Given as :

The function f(x)

f (x) = $\dfrac{kcosx}{\pi -2x}$                x  ≠ $\dfrac{\pi }{2}$

Let The value of k = a  for  x = $\dfrac{\pi }{2}$

According to question

f (x) = $\dfrac{kcosx}{\pi -2x}$    

      = $\dfrac{k}{2}$  [ $\dfrac{cosx}{\dfrac{\pi }{2} -x}$  ]

      = $\dfrac{k}{2}$ [ $\dfrac{sin(\dfrac{\pi }{2}-x) }{\dfrac{\pi }{2} -x}$  ]

now,

$\lim x\underset{}{\rightarrow}_{\dfrac{\Pi }{2}}$ f (x) = $\lim x\underset{}{\rightarrow}_{\dfrac{\Pi }{2}}$ $\dfrac{k}{2}$ [ $\dfrac{sin(\dfrac{\pi }{2}-x) }{\dfrac{\pi }{2} -x}$  ]

Or,                  = $\dfrac{k}{2}$ $\lim x\underset{}{\rightarrow}_{\dfrac{\Pi }{2}}$  $\dfrac{sin(\dfrac{\pi }{2}-x) }{\dfrac{\pi }{2} -x}$

                      = $\dfrac{k}{2}$  × 1

                      = $\dfrac{k}{2}$

if  x is continues at $\dfrac{\pi }{2}$

Then  $\dfrac{k}{2}$ = $\lim x\underset{}{\rightarrow}_{\dfrac{\Pi }{2}}$ f (x)

i.e      $\dfrac{k}{2}$  = 3

∴        k = 2 × 3

Or,    k = 6

So, The value of k for the given function = k = 6

Hence, The value of k for the given function is 6  . Answer