MATHEMATICAL ANALISYS. Answer with true or false to the following sentences and argue your answers: 1. Every continuous function defined on an open interval can be uniformly approximated by polynomials. 2. Any continuous function defined on a closed interval can be uniformly approximated by polynomials. 3. Every continuous function is Riemann Stieljes integrable with respect to a function of bounded variable. 4. Every function of a continuous real variable is a measurable function with respect to the Borel sigma algebra. 5. A function with a countably infinite number of discontinuities cannot be Lebesgue integrable Please be as clear as possible explaining your answers. Thank you very

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A: Since you have asked multiple questions in single request.so we will answering only first question.…

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A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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A: There is no error in the proof of above statement .

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A: Let us first draw the graph of function.

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