Show that f is continuous on (-∞, ∞). (₁-x² if x ≤ 1 In(x) if x > 1 On the interval (-∞, 1), f is ---Select--- On the interval (1, ∞), fis ---Select--- At x = 1, f(x) = = lim f(x) = lim x → 1- x-1- and lim f(x) = lim x→1+ X→1+ so lim f(x) = x-1 = = e function; therefore f is continuous on (-∞, 1). function; therefore f is continuous on (1, ∞0). . Also, f(1) = Thus, f is continuous at x = 1. We conclude that f is continuous on (-∞, ∞).
Show that f is continuous on (-∞, ∞). (₁-x² if x ≤ 1 In(x) if x > 1 On the interval (-∞, 1), f is ---Select--- On the interval (1, ∞), fis ---Select--- At x = 1, f(x) = = lim f(x) = lim x → 1- x-1- and lim f(x) = lim x→1+ X→1+ so lim f(x) = x-1 = = e function; therefore f is continuous on (-∞, 1). function; therefore f is continuous on (1, ∞0). . Also, f(1) = Thus, f is continuous at x = 1. We conclude that f is continuous on (-∞, ∞).
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Transcribed Image Text:Show that f is continuous on (-∞, ∞).
f(x) = {1- x² ifx ≤ 1
if x > 1
On the interval (-∞, 1), f is ---Select---
On the interval (1, ∞), fis
---Select---
At x = 1,
lim f(x) = lim
X→ 1-
x-1-
and
lim f(x) =
= lim
X-1
+
X→ 1+
so lim f(x) =
X-1
Also, f(1) =
function; therefore f is continuous on (-∞, 1).
function; therefore f is continuous on (1, ∞).
I
Thus, f is continuous at x = 1. We conclude that f is continuous on (-∞, ∞).
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