Consider the following Fx inx 1 x0 4 x2 x Solutionlimx0fx

Consider the following. F(x) = {in(x + 1), x>_0 4 - x2, x

lim_x->0^-f(x)

lim_x->0^-(4-x²)

=4-0²

lim_x->0⁺f(x)

=lim_x->0⁺ln(x+1)

=ln(0+1)

=ln1

lim_x->0^-f(x)lim_x->0⁺f(x)

so function discontinous at x =0

no removable discontinuity

$Consider the following. F(x) = {in(x + 1), x>_0 4 - x2, x Solutionlimx->0-f(x) limx->0-(4-x2) =4-02 =4 limx->0+f(x) =limx->0+ln(x+1) =ln(0+1) =l$