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Let / g C\a, ft], and let p be in the open interval (a, ft). a. Suppose f{p) ^ 0. Show
Chapter 1, Problem 30(choose chapter or problem)
Let / g C\a, ft], and let p be in the open interval (a, ft). a. Suppose f{p) ^ 0. Show that a 5 > 0 exists with /(x) ^ 0, for all x in [/? 5, /? + 5], with fp (5, p + <5] a subset of [a, ft], b. Suppose /(p) = 0 and ft > 0 is given. Show that a 5 > 0 exists with |/(x)| < ft, for all x in [p (5, p + >5], with [p 5, p + 3] a subset of [a, ft].
Questions & Answers
QUESTION:
Let / g C\a, ft], and let p be in the open interval (a, ft). a. Suppose f{p) ^ 0. Show that a 5 > 0 exists with /(x) ^ 0, for all x in [/? 5, /? + 5], with fp (5, p + <5] a subset of [a, ft], b. Suppose /(p) = 0 and ft > 0 is given. Show that a 5 > 0 exists with |/(x)| < ft, for all x in [p (5, p + >5], with [p 5, p + 3] a subset of [a, ft].
ANSWER:Step 1 of 3
A function is said to be continuous at , if for every , there exists a , such that