#### Question

Find the values of *k *so that the function *f* is continuous at the indicated point.

`f(x) = {((kcosx)/(pi-2x), "," if x != pi/2),(3, "," if x = pi/2):} " at x =" pi/2`

#### Solution 1

The given function *f* is `f(x) = {((kcosx)/(pi-2x), "," if x != pi/2),(3, "," if x = pi/2):} " at x " pi/2`

#### Solution 2

The given function *f* is `f(x) = {((kcosx)/(pi-2x), "," if x != pi/2),(3, "," if x = pi/2):}`

The given function *f* is continuous at ,`x= pi/2` if *f* is defined at `x= pi/2`and if the value of the *f* at `x= pi/2` equals the limit of *f* at `x= pi/2`

It is evident that *f *is defined at `x= pi/2` and `f(pi/2) = 3`

Therefore, the required value of *k* is 6.

Is there an error in this question or solution?

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Find the Values Of K So that the Function F Is Continuous at the Indicated Point. F(X) = {((Kcosx)/(Pi-2x), If X != Pi/2),(3, If X = Pi/2) at X Pi/2 Concept: Algebra of Continuous Functions.

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