GHW2 - for any From that relationship find if is 1 nm(nanometer Section 2.5 Continuity 1(6 pts Circle all functions that are everywhere

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MATH 2413 Graded Homework #2 GHW2 11 August 2011 Due 9/19 in Lecture Work is to be done in a Blue book per the syllabus Section 2.4 The precise definition of Limit 1. (8 pts) Complete the epsilon delta definition of limit. Let f be a function defined on some open interval that contains the number a , except possibly at a itself. Then we say that the limit of as x approaches a is L , and we write ) ( x f L x f a x = ) ( lim ____________________________________________________________________ _____________________________________________________________________ 2. (12 pts) Given the limit statement 19 ) 7 4 ( lim 3 = + x x (a) Write the inequalities ε < L x f ) ( and δ < a x as they pertain to this statement, simplify. (b) Illustrate the definition of limit by finding a number that corresponds to 1 . 0 = , repeat for 002 . 0 = . (c) Deduce a relationship between and that would allow you to compute
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Unformatted text preview: for any . From that relationship, find if is 1 nm (nanometer). Section 2.5 Continuity 1. (6 pts) Circle all functions that are everywhere continuous. (write all of them in your bluebook ) (a) the cube root function (b) (c) 9 2 3 ) ( − = x e x f ) ( = x f (d) (e) (f) x x x f cos sin ) ( = ) ln( ) ( 2 x x f = 1 ) ( 2 + = x x x f 2. (8 pts) Find the numbers at which f is discontinuous. At which of these numbers is f continuous from the left, from the right, or neither? ⎪ ⎩ ⎪ ⎨ ⎧ ≥ − < < < − − = 2 3 2 4 3 ) ( 2 x if x x if x if x x x f 3. (6 pts) For what value(s) of the constant a is the function f continuous everywhere? ⎩ ⎨ ⎧ ≥ < + + + = 4 4 ) 2 ( ) ( 2 x x x a a x a x f Page 1 of 1...
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This note was uploaded on 11/16/2011 for the course MATH 2413 taught by Professor . during the Fall '11 term at University of Texas at Dallas, Richardson.

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