mreditor16
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Proof outline for 74 (c):
PROOF OUTLINE:
Let.
By definition of limits to infinity, there existsuch that
whenever
and whenever
. So
, and:
(1)
(2).
By the extreme value theorem (since f is continuous),attains a maximum value
on
.
Sincewhen
, this maximum
satisfies
. (3)
(1), (2) and (3) imply that f attains a maximum value on, namely
.
I did not use the hint, I did this instead:
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But using the hint:
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How did we conclude that there exists a such thatI hope this helps
.