Question 4:14 Ma(a) Let f and g be functions such that f(x) < g(x) for all x in theinterval (a, b), (with a < b). Show that ifL = lim f(x) and M = lim g(x)Ta+x→a+both exist, then L< M.(b) Using the formal definition of limit, show that if lim an = +oand r < 0, then lim r an = -00.

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Answered: O Let f and g be functions such that…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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O Let f and g be functions such that f(x) < g(x) for all æ in the interval (a, b), (with a < b). Show that if L = lim f(x) and M = lim g(x) Ta+ aa+ both exist, then L< M. O Using the formal definition of limit, show that if lim an = +o and r < 0, then lim r an = -o∞.