Suppose lim f(x) = L and lim g(x) M. Prove that lim [f(x) - g(x)] = L- M. Xa Xa Begin by writing lim [f(x)- g(x)] as a sum. Xa lim [f(x) - g(x)] lim [f(x) + (g(x)] %3D Xa Xa

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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Let f(x)= x+5 and note that lim f(x) = 5. For each value of e given below, use a graphing utility to find the maximum value of & > 0 such that f(x)- 5| <ɛ whenever 0</x-0<8.
(a) e 2
(b) e=1
.....
(b) Choose the correct answer below.
O A. 8=1.414
B. 8=1
C. 6 =1.667
D. There is no such value of
Transcribed Image Text:Let f(x)= x+5 and note that lim f(x) = 5. For each value of e given below, use a graphing utility to find the maximum value of & > 0 such that f(x)- 5| <ɛ whenever 0</x-0<8. (a) e 2 (b) e=1 ..... (b) Choose the correct answer below. O A. 8=1.414 B. 8=1 C. 6 =1.667 D. There is no such value of
Suppose lim f(x) =L and lim g(x) =M. Prove that lim [f(x) - g(x)] = L- M.
%3D
Xa
Xa
Xa
Begin by writing lim [f(x)- g(x)] as a sum.
Xa
lim [f(x)-g(x)]
= lim [f(x) + ( g(x)]
Xa
Xa
Transcribed Image Text:Suppose lim f(x) =L and lim g(x) =M. Prove that lim [f(x) - g(x)] = L- M. %3D Xa Xa Xa Begin by writing lim [f(x)- g(x)] as a sum. Xa lim [f(x)-g(x)] = lim [f(x) + ( g(x)] Xa Xa
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