If f(x) = [x]] + [-x], show that lim f(x) exists but is not equal to f(2). X-2

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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If f(x) = [x]] + [-x], show that lim f(x) exists but is not equal to f(2).
x→ 2
The graph of f(x) = [x] + [-x] is the same as the graph of g(x) = -1 with holes at each integer, since f(a) =
However,
lim f(x) =
X-2
f(2)= [2] + [[-2]] = 2 +
so lim f(x) + f(2).
x-2
and
lim f(x) =
x 2
, so lim f(x) =
x→2
for any integer a. Also,
Transcribed Image Text:If f(x) = [x]] + [-x], show that lim f(x) exists but is not equal to f(2). x→ 2 The graph of f(x) = [x] + [-x] is the same as the graph of g(x) = -1 with holes at each integer, since f(a) = However, lim f(x) = X-2 f(2)= [2] + [[-2]] = 2 + so lim f(x) + f(2). x-2 and lim f(x) = x 2 , so lim f(x) = x→2 for any integer a. Also,
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