Q1:Preview1. Let I CR be any interval (open, closed, half-open, bounded or unbounded). If f: I → R iscontinuous, and for all r, s E QNI with r < swe have f(r) < f(s), then for all x < y E Iwe have f(x) < f(y).(That is show that if f onI is strictly monotoneincreasing, then so is f.)2. Let f : R → R be an exponential function withf(1). Show that f is strictlymonotone increasing if a > 1 and strictlymonotone decreasing if a < 1.base a =

Answered: Image /qna-images/answer/c19fd9a1-f9a4-4e86-93be-4021fdfb00e3.jpg

Preview 1. Let I CR be any interval (open, closed, half- open, bounded or unbounded). If f: I → R is continuous, and for all r, s E QnI with r < s we have f(r) < f(s), then for all x < y € I we have f(x) < f(y). (That is show that if floor is strictly monotone

Preview 1. Let I CR be any interval (open, closed, half- open, bounded or unbounded). If f: I → R is continuous, and for all r, s E QnI with r < s we have f(r) < f(s), then for all x < y € I we have f(x) < f(y). (That is show that if floor is strictly monotone

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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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Q1:
Preview
1. Let I CR be any interval (open, closed, half-
open, bounded or unbounded). If f: I → R is
continuous, and for all r, s E QNI with r < s
we have f(r) < f(s), then for all x < y E I
we have f(x) < f(y).
(That is show that if f onI is strictly monotone
increasing, then so is f.)
2. Let f : R → R be an exponential function with
f(1). Show that f is strictly
monotone increasing if a > 1 and strictly
monotone decreasing if a < 1.
base a =

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