`{{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+3/2, if l lt x le 2):}` at `x = 1`

Explanation

Given function `{{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+3/2, if l lt x le 2):}`
at the point `x=1`
LHL at `x=1`,
`lim_(x->1^-)f(x)`
`=lim_(h->1^-)h^2/2`
`=1/2`
RHL at `x=1`,
`lim_(x->1^+)f(x)`
`=lim_(h->1^+)2h^2-3h+3/2`
`=2-3+3/2`
`=1/2`
also `f(1)=1/2`
here, `LHL=RHL = functional value`
therefore this function is continuous at `x=1`