Show that

f

is continuous on

(-\\\\infty ,\\\\infty )

.\

f(x)={(1-x^(2) if x1):}

\ On the interval

(-\\\\infty ,1),f

is ] function; therefore

f

is continuous on

(-\\\\infty ,1)

.\ On the interval

(1,\\\\infty ),f

is function; therefore

f

is continuous on

(1,\\\\infty )

.\ At

x=1

,\

\\\\lim_(x->1^(-))f(x)=\\\\lim_(x->1^(-))(,)=

\ and\

\\\\lim_(x->1^(+))f(x)=\\\\lim_(x->1^(+))()=

\ so

\\\\lim_(x->1)f(x)=

\ Also,

f(1)=

Show that f is continuous on (,). f(x)={1x2ln(x)ifx1ifx>1 On the interval (,1),f is function; therefore f is continuous on (,1). On the interval (1,),f is function; therefore f is continuous on (1,). At x=1, limx1f(x)=limx1()= and limx1+f(x)=limx1+()= so limx1f(x)= Also, f(1)=