Suppose f(x) and g(x) are continuous functions, and | f(x) g(x) if x > 0, h(x) : if x < 0 . if x = 0 If h(x) is not continuous at x = 0, which of the following statements must be FALSE? а. g(0) 3D 2 O b. limx-0 h(x) exists and equals 2 c. limx¬0f(x) = 2 %3D d. limx+¬0f(x) = limx-→0g(x) e. limx-0 h(x) exists X→0

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Suppose f(x) and g(x) are continuous functions, and
f(x)
if x > 0,
h(x)
g(x)
if x < 0 .
if x = 0
If h(x) is not continuous at x =
0, which of the
following statements must be FALSE?
а. g(0)
= 2
O b. limx→0 h(x) exists and equals 2
c. limx-0f(x) = 2
d. limxt-0f(x) = limx-→0g(x)
е. lim,x-0 h(х) exists
Transcribed Image Text:Suppose f(x) and g(x) are continuous functions, and f(x) if x > 0, h(x) g(x) if x < 0 . if x = 0 If h(x) is not continuous at x = 0, which of the following statements must be FALSE? а. g(0) = 2 O b. limx→0 h(x) exists and equals 2 c. limx-0f(x) = 2 d. limxt-0f(x) = limx-→0g(x) е. lim,x-0 h(х) exists
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