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Find the value of k so that the function...

Find the value of k so that the function f defined by `f(x)={(kcosx)/(pi-2x),3\ \ \ ,\ \ \ \ \ \ \ \ \ \ "if"\ \ x\ !=pi/2"if"\ x=pi/2` is continuous at `x=pi/2`

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For `f(x)` to be continuous at `x = a`,
`Lim_(x->a) f(x) = f(a)`
Here, `f(x) = (kcosx)/(pi-2x)`
`f(pi/2) = 3`
As, `f(x)` is continuous at `x = pi/2`.
`:. Lim_(x->pi/2) (kcosx)/(pi-2x) = 3`
As left side of the equation is a `0/0` form, so we will apply L`'`Hospital rule.
`:. Lim_(x->pi/2) (-ksinx)/(-2) = 3`
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Knowledge Check

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