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Let f E C(0, 1). Suppose that lim f(x)= lim f(x)=+∞. Show that f acheives its minimum in (0, 1). Hint: x→0+ take a minimizing sequence.

Let f E C(0, 1). Suppose that lim f(x)= lim f(x)=+∞. Show that f acheives its minimum in (0, 1). Hint: x→0+ take a minimizing sequence.

Advanced Engineering Mathematics
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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Let f E C(0,1). Suppose that lim f(x) lim f(x) = +o. Show that f acheives its minimum in (0, 1). Hint: T→1- take a minimizing sequence.
Transcribed Image Text:Let f E C(0,1). Suppose that lim f(x) lim f(x) = +o. Show that f acheives its minimum in (0, 1). Hint: T→1- take a minimizing sequence.
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