Question:

12. (0.12/0.5 Points] DETAILS PREVIOUS ANSWERS SCALCET9 2.5.041. Show that f is continuous on (-00,00). f(x) - { ſ1 - x2 if x S

12. (0.12/0.5 Points]
DETAILS
PREVIOUS ANSWERS
SCALCET9 2.5.041.
Show that f is continuous on (-00,00).
f(x)
- {
ſ1 - x2 if x S 1
In(x) if x > 1
On the interval (-0, 1), f is a polynomial
function; therefore f is continuous on (-00, 1).
On the interval (1, 0), f is a logarithmic
function; therefore f is continuous on (1, 0).
At x = 1,
lim f(x) = lim
x-1
x-1
D-
and
lim f(x) = lim
1)-
xtit
x+1+
so lim f(x) =
x1
Also, f(1) =
Thus, f is continuous at x = 1. We conclude that f is continuous on (-0,co).

12. (0.12/0.5 Points] DETAILS PREVIOUS ANSWERS SCALCET9 2.5.041. Show that f is continuous on (-00,00). f(x) - { ſ1 - x2 if x S 1 In(x) if x > 1 On the interval (-0, 1), f is a polynomial function; therefore f is continuous on (-00, 1). On the interval (1, 0), f is a logarithmic function; therefore f is continuous on (1, 0). At x = 1, lim f(x) = lim x-1 x-1 D- and lim f(x) = lim 1)- xtit x+1+ so lim f(x) = x1 Also, f(1) = Thus, f is continuous at x = 1. We conclude that f is continuous on (-0,co).