Find the values of k so that the function f is continuous at the indicated point in `f(x)={k x^2, if""xlt=2 3, if""""x >2` at `x" "=" "2` .

Explanation

`f(x) = {{:(kx^(2)"," if x le 2),(3", " if x gt 2):}`
at x = 2
`f( 2) = k(2)^(2)= 4 k`
R.H.L. `underset (x to 2^(+))(lim)f(x)`
Let 2+ h = x
`rArr 2 + h to 2`
`rArr h to o`
`= underset (h to 0) (lim) f(2 + h) = underset (h to 0) (lim)3=3`
`:'` f(2) is continuous at x = 2
`:.` f(2) is = R.H.L.
`rArr 4k = 3`
`rArr k = (3)/(4).`