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Prove that if $f(x)$ is continuous on the closed interval $[a,b]$ , then $f(x)$ is uniformly continuous on $[a,b]$ .

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Lesson Parent:

Problem:

Answer:

It is true that if $f(x)$ is continuous on the closed interval $[a,b]$ , then $f(x)$ is uniformly continuous on $[a,b]$ .

Solution:

This proof is extremely hard and almost never required for a beginning Calculus course - even a beginning Calculus course for mathematics majors. You can safely ignore this proof, but be aware that it is an important proof for showing that continuous functions are integrable.

We don't have all the info to complete this proof at the moment . . .

Prove that if f(x)f(x) is continuous on the closed interval [a,b][a,b], then f(x)f(x) is uniformly continuous on [a,b][a,b].

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SAMPLE SOLUTION

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Prove that if $f(x)$ is continuous on the closed interval $[a,b]$ , then $f(x)$ is uniformly continuous on $[a,b]$ .