Determine if each statement is true or false, and briefly explain why: A. Let I be an interval of R and f, g: I → R two uniformly continuous functions. We have f + g uniformly continuous. B.Let I be an interval of R and f, g: I → R two uniformly continuous functions. We have fg uniformly continuous.

Advanced Engineering Mathematics
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Determine if each statement is true or false, and briefly explain why:

A. Let I be an interval of R and f, g: I → R two uniformly continuous functions. We have f + g uniformly continuous.

B.Let I be an interval of R and f, g: I → R two uniformly continuous functions. We have fg uniformly continuous.

C. Let I, J are intervals of R and f: I∪J → R. If the restrains of f to I and J are uniformly continuous then f is uniformly continuous.

D. Let (Ai)iEI a family of intervals of R and I=UiEIAi. If all the restrains of f:Ai→R are uniformly continuous then f is uniformly continuous.

E.The exponential function is not uniformly continuous over R

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