2. Assume additionally that f E C[a, b]. Show that there is E (a, b) such that | F(x)g(x) dæ = f(€) / g(x) dæ. Hint: use the intermediate value property for f.
2. Assume additionally that f E C[a, b]. Show that there is E (a, b) such that | F(x)g(x) dæ = f(€) / g(x) dæ. Hint: use the intermediate value property for f.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...
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![Let f, g E R[a, b]. Suppose that g > 0 on [a, b].
1. Show that
inf f ·
[a,b)
| f(x)g(x) dæ < sup f
[a,b]
g(x) dæ <
g(x) dx.
a
2. Assume additionally that f E C[a,b]. Show that there is § E (a, b) such that
| f(x)g(x) dx = f(£) / g(x) dx.
Hint: use the intermediate value property for f.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab72d35c-8dab-4035-b354-39390c2a5b5a%2Fd08c9aad-18ed-428c-bfe4-a3388bb5bfb2%2Fd9e9szw_processed.png&w=3840&q=75)
Transcribed Image Text:Let f, g E R[a, b]. Suppose that g > 0 on [a, b].
1. Show that
inf f ·
[a,b)
| f(x)g(x) dæ < sup f
[a,b]
g(x) dæ <
g(x) dx.
a
2. Assume additionally that f E C[a,b]. Show that there is § E (a, b) such that
| f(x)g(x) dx = f(£) / g(x) dx.
Hint: use the intermediate value property for f.
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