Prove that f: R→ R is continuous. 2. Suppose that the function f: [0, 1] → R is continuous and that f(r) ≥ 2 if 0 ≤r < 1. Show that f(1) ≥ 2.
Prove that f: R→ R is continuous. 2. Suppose that the function f: [0, 1] → R is continuous and that f(r) ≥ 2 if 0 ≤r < 1. Show that f(1) ≥ 2.
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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Solve question 2 using sequences
![-1² if x ≤0
Prove that f: R→ R is continuous.
2. Suppose that the function f : [0,1] → R is continuous and that f(x) ≥ 2 if 0 < x < 1.
Show that f(1) ≥ 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30e714d6-c3d6-4fe9-9c10-b4b8c64f125f%2Fcd867eb7-b65f-44bd-81b8-fe105835e602%2Fq3d6uwa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:-1² if x ≤0
Prove that f: R→ R is continuous.
2. Suppose that the function f : [0,1] → R is continuous and that f(x) ≥ 2 if 0 < x < 1.
Show that f(1) ≥ 2.
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