Math

Limits and Continuity Solutions

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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).