4 1. Written Part True/false. For each statement, you should either give a proof or an counter example. (a) f(x) is an increasing function defined on some interval I ER, then f(x) has its inverse function and f-¹(x) is also increasing. (b) f(x) > 0 for all x € R. If limx→o f(x) exists and is equal to LER, then L > 0. (c) Assume that f(x) and g(x) are defined on x # 0 and lim [f(x) + g(x)] = +∞, then lim o f(x) = +∞ or limo g(x) = +∞, or both approach +∞o.
4 1. Written Part True/false. For each statement, you should either give a proof or an counter example. (a) f(x) is an increasing function defined on some interval I ER, then f(x) has its inverse function and f-¹(x) is also increasing. (b) f(x) > 0 for all x € R. If limx→o f(x) exists and is equal to LER, then L > 0. (c) Assume that f(x) and g(x) are defined on x # 0 and lim [f(x) + g(x)] = +∞, then lim o f(x) = +∞ or limo g(x) = +∞, or both approach +∞o.
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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![4 Written Part
True/false. For each statement, you should either give a proof or an
counter example.
(a) f(x) is an increasing function defined on some interval I ɛ R,
then f(x) has its inverse function and f-¹(x) is also increasing.
1.
(b) f(x) > 0 for all x € R. If limx→o f(x) exists and is equal to
LER, then L > 0.
(c) Assume that f(x) and g(x) are defined on x ‡ 0 and
lim[ƒ(x) + g(x)] = +∞0,
then limx→o f(x) = +∞ or limx→0 g(x)
=
+∞, or both approach +∞.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74b84872-1fb7-4d60-8950-d76f52e19a4e%2Fb8b99dc4-8002-4e30-bb92-a60be3de87fe%2Fu3t7s6e_processed.png&w=3840&q=75)
Transcribed Image Text:4 Written Part
True/false. For each statement, you should either give a proof or an
counter example.
(a) f(x) is an increasing function defined on some interval I ɛ R,
then f(x) has its inverse function and f-¹(x) is also increasing.
1.
(b) f(x) > 0 for all x € R. If limx→o f(x) exists and is equal to
LER, then L > 0.
(c) Assume that f(x) and g(x) are defined on x ‡ 0 and
lim[ƒ(x) + g(x)] = +∞0,
then limx→o f(x) = +∞ or limx→0 g(x)
=
+∞, or both approach +∞.
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