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.
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: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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