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Consider two functions f eg defined om R. (a) Establish whether it is possible to compute the following limits with the available information: (i) lim エ→0 2f(r) + g(x) 3 + 2x² with f(x) = o(x²) and g(x) = o(x*) for r0. %3D (ii) lim エー+00 2f(x) + g(x) 3+2x2 with f(r) = o(r²) and g(r) o(r) for r+. %3D r2 sin(g(x))+ f(r) sin r+ r] 2.r + g(x)+ f(r) (iii) lim with f(r) o(r) and g(r) - o(r) for r 0.

Consider two functions f eg defined om R. (a) Establish whether it is possible to compute the following limits with the available information: (i) lim エ→0 2f(r) + g(x) 3 + 2x² with f(x) = o(x²) and g(x) = o(x*) for r0. %3D (ii) lim エー+00 2f(x) + g(x) 3+2x2 with f(r) = o(r²) and g(r) o(r) for r+. %3D r2 sin(g(x))+ f(r) sin r+ r] 2.r + g(x)+ f(r) (iii) lim with f(r) o(r) and g(r) - o(r) for r 0.

Calculus: Early Transcendentals
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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Consider two functions f e g defined om R. (a) Establish whether it is possible to compute the following limits with the available information: 2f(x) + g(x) 13+2x2 (i) lim with f(x) = o(²) and g(x) = o(r) for r0. 2f(x) + g(x) 3+2x2 (ii) lim with f(r) = o(x²) and g(x) = o(r*) for r → +x. %3D sin(g(r))+ f(r) sin r+ r 2.r + g(x) + f"(x) (iii) lim with f(r) - o(r) and g(r) - o() for r 0. (b) Prove that: if f o(r) per r+, then f(r) = o(r*+1) per r → +x.
Transcribed Image Text:Consider two functions f e g defined om R. (a) Establish whether it is possible to compute the following limits with the available information: 2f(x) + g(x) 13+2x2 (i) lim with f(x) = o(²) and g(x) = o(r) for r0. 2f(x) + g(x) 3+2x2 (ii) lim with f(r) = o(x²) and g(x) = o(r*) for r → +x. %3D sin(g(r))+ f(r) sin r+ r 2.r + g(x) + f"(x) (iii) lim with f(r) - o(r) and g(r) - o() for r 0. (b) Prove that: if f o(r) per r+, then f(r) = o(r*+1) per r → +x.
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