Let I be an open interval containing 0, and let f : I R be any function that is bounded on I. Define a new function g : I R by g(x) := xf(x).<\/p>
(a) Prove using the e- definition of continuity that g is continuous at x = 0. <\/p>
<\/p>
(b) Suppose a not equal to 0, a I. Prove using the e- definition of continuity that if f is continuous at x = a then g is also continuous at x = a.<\/p>", "transcribed_text": "", "related_book": { "title": "Intermediate Accounting", "isbn": "978-1118735329, 9781118726327, 1118735323, 1118726324, 978-0176509736", "edition": "10th Canadian Edition, Volume 1", "authors": "Donald Kieso, Jerry Weygandt, Terry Warfield, Nicola Young, ", "cover_image": "https:\/\/dsd5zvtm8ll6.cloudfront.net\/si.question.images\/book_images\/528.jpg", "uri": "\/textbooks\/intermediate-accounting-10th-canadian-edition-volume-1-528", "see_more_uri": "" }, "free_related_book": { "isbn": "1466319984", "uri": "\/textbooks\/building-your-paparazzi-business-1st-edition-978-1466319981-362941", "name": "Building Your Paparazzi Business", "edition": "1st Edition" }, "question_posted": "2024-06-12 07:14:57", "see_more_questions_link": "\/study-help\/questions\/sciences-physics-2023-November-14", "step_by_step_answer": "The Answer is in the image, click to view ...", "students_also_viewed": [ { "url": "\/in-exercises-find-a-ptlu-factorization-of-the-given-matrix", "description": "In Exercises, find a PTLU factorization of the given matrix A. a. b. 413 123 2210 1311 0121 0101", "stars": 3 }, { "url": "\/presented-below-are-the-main-section-headings-of-the-balance", "description": "Presented below are the main section headings of the balance sheet: a. 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