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5. Choose and work either (a) or (b), NOT BOTH. (a) Show that e" > 1+x for x > 0. (HINT: Mean Value Theorem on [0, x])

5. Choose and work either (a) or (b), NOT BOTH. (a) Show that e" > 1+x for x > 0. (HINT: Mean Value Theorem on [0, x])

Linear Algebra: A Modern Introduction
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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Real Analysis 1
5. Choose and work either (a) or (b), NOT BOTH. (a) Show that e > 1+ x for x > 0. (HINT: Mean Value Theorem on [0, x]) (b) Let f : [0, 2] →R be defined by f(x) = 3" – 2x2 – 1. Show that this function attains extreme values in the interior of the interval [0, 2].
Transcribed Image Text:5. Choose and work either (a) or (b), NOT BOTH. (a) Show that e > 1+ x for x > 0. (HINT: Mean Value Theorem on [0, x]) (b) Let f : [0, 2] →R be defined by f(x) = 3" – 2x2 – 1. Show that this function attains extreme values in the interior of the interval [0, 2].
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