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

Answer

N/a

Explanation

We have, `{{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+3/2, if l lt x le 2):}` at `x = 1`
At `x = 1, HL = underset(xrarr1^(-))(lim)(x^(2))/(2)=underset(hrarr0)(lim)((1-h)^(2))/(2)`
`= underset(hrarr0)lim(1+h^(2)-2h)/(2)=(1)/(2)`
RHL `= underset(xrarr1^(+))lim(2x^(2)-3x+3/2)`
`= underset(hrarr0)lim[2(1+h)^(2)-3(1+h)+3/2]`
`= underset(hrarr0)(lim)(2+2h^(2)+4h-3-3h+3/2)=-1+3/2 = 1/2`
and `f(1) = (1^(2))/(2)=1/2`
Hence , `f(x)` is continuous at `x = 1`.