Examine the continuity of the function `f(x)=2x^2-1`at `x = 3`.

Explanation

`f(x) = 2x ^(2) -1`
at x = 3
Let x = 3 + h
`rArr 3 + h to 3 `
`rArr h to 0 `
`f(3) = 2(3)^(2) - 1 = 17 `
L.H.L. = `underset (x to 3^(-))(lim) f(x)`
=`underset ( hto 0)(lim) f(3 - h)`
=`underset ( hto 0)(lim)2(3 - h )^(2)-1`
` 2(3 - 0 )^(2) - 1 = 17`
R.H.L. = =`underset ( X to 3^(+))(lim)f(x)`
Let x = 3 + h
`rArr 3 + h to 3 `
`rArr h to 0 `
=`underset ( h to 0)(lim)f(3 + h )`
=`underset ( h to 0)(lim)2(3 + h )^(2)-1 `
`= 2(3 + 0 )^(2) - 1 = 17`
`:'` L.H.L. = f(3) = R.H. L.
`:.` f(x) is contnuous at x = 3 .