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Determine the Value of 'K' for Which the Following Function is Continuous at X = 3 F(X)=(X+3)2−36/X−3 - Mathematics

Sum

Determine the value of 'k' for which the follwoing function is continuous at x = 3

`f(x) = {(((x+3)^2-36)/(x-3),  x != 3), (k,  x =3):}`

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Solution

Given f(x) is continuous at x = 3

`:. lim_(x->3) f(x)= k`

`lim_(x-> 3) ((x+3)^2 - 36)/(x-3) = k`

`lim_(x->3) ((x+3)^2 - 6^2)/(x-3) = k`

`lim_(x->3) ((x+3+6)(x+3-6))/(x-3) = k`

`lim_(x->3) ((x - 3)(x + 9))/(x-3)`

`lim_(x->3) (x + 9) = 3 + 9`

k = 12

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