(4) Let f(x) be the function with domain R given by the rule X if x EQ, and 0 if x # Q. f(x) = = (a) Prove that lime-o f(x) = 0. (b) Prove that if a 0, then limx→a f(x) does not exist. DEFINITION: Let f be a function and a E R. We say that the limit of f(x) as x approaches a from the right is L provided: For every > 0, there is some 8 >0 such that for all x satisfying a < x
(4) Let f(x) be the function with domain R given by the rule X if x EQ, and 0 if x # Q. f(x) = = (a) Prove that lime-o f(x) = 0. (b) Prove that if a 0, then limx→a f(x) does not exist. DEFINITION: Let f be a function and a E R. We say that the limit of f(x) as x approaches a from the right is L provided: For every > 0, there is some 8 >0 such that for all x satisfying a < x
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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