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3. Let f A → X be a function such that A CX. Show that if A is compact, then the range of f defined by f(A) = {f(x) : x € A} is bounded.

3. Let f A → X be a function such that A CX. Show that if A is compact, then the range of f defined by f(A) = {f(x) : x € A} is bounded.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter5: Graphs And The Derivative
Section5.3: Higher Derivatives, Concavity, And The Second Derivative Test
Problem 61E
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Let f: A→ X be a function such that A CX. Show that if A is compact, then the range of f defined by f(A) = {f(x) : x E A} is bounded.
Transcribed Image Text:Let f: A→ X be a function such that A CX. Show that if A is compact, then the range of f defined by f(A) = {f(x) : x E A} is bounded.
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