For this problem, you will need to recall Definition 7.10 and Lemma 7.9. Assume that bounded functions f, g: [a, b] → R are integrable. (a) In this part you will show that if f(x) > 0 for all x € [a, b], then [ f(x) dx > 0 a by completing the following steps: (i) Show that L(f) ≥ 0. (ii) Use definition 7.10 to show that ·b [* a f(x) dx > 0.
For this problem, you will need to recall Definition 7.10 and Lemma 7.9. Assume that bounded functions f, g: [a, b] → R are integrable. (a) In this part you will show that if f(x) > 0 for all x € [a, b], then [ f(x) dx > 0 a by completing the following steps: (i) Show that L(f) ≥ 0. (ii) Use definition 7.10 to show that ·b [* a f(x) dx > 0.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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