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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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.
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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