M408K Hm. 4 Solutions

M408K Hm. 4 Solutions - Mahon, Kevin Homework 4 Due: Sep 22...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Mahon, Kevin Homework 4 Due: Sep 22 2005, 3:00 am Inst: Edward Odell 1 This print-out should have 24 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Functions f and g are defined on (- 10 , 10) by their respective graphs in 2 4 6 8- 2- 4- 6- 8 4 8- 4- 8 f g Find all values of x where the sum, f + g , of f and g is continuous, expressing your answer in interval notation. 1. (- 10 ,- 2) [ (- 2 , 4) [ (4 , 10) 2. (- 10 , 4) [ (4 , 10) 3. (- 10 ,- 2] [ [4 , 10) 4. (- 10 , 10) 5. (- 10 ,- 2) [ (- 2 , 10) correct Explanation: Since f and g are piecewise linear, they are continuous individually on (- 10 , 10) except at their jumps, i.e. , at x = 4 in the case of f and x = 4 ,- 2 in the case of g . But the sum of continuous functions is again continuous, so f + g is certainly continuous on (- 10 ,- 2) [ (- 2 , 4) [ (4 , 10) . The only question is what happens at x = 4 ,- 2. To do that we have to check if lim x x- { f ( x ) + g ( x ) } = f ( x ) + g ( x ) = lim x x + { f ( x ) + g ( x ) } . Now at x = 4, lim x 4- { f ( x ) + g ( x ) } = 1 = f (4) + g (4) = lim x 4+ { f ( x ) + g ( x ) } , while at x =- 2, lim x - 2- { f ( x ) + g ( x ) } =- 2 6 =- 5 = lim x - 2+ { f ( x ) + g ( x ) } . Thus, f + g is continuous at x = 4, but not at x =- 2. Consequently, on (- 10 , 10) the sum f + g is continuous at all x in (- 10 ,- 2) [ (- 2 , 10) . keywords: Stewart5e, 002 (part 1 of 1) 10 points Below is the graph of a function f . 2 4 6- 2- 4- 6 2 4 6 8- 2- 4 Mahon, Kevin Homework 4 Due: Sep 22 2005, 3:00 am Inst: Edward Odell 2 Use the graph to determine all the values of x on (- 6 , 6) at which f fails to be continuous. 1. x =- 3 , 2 correct 2. no values of x 3. x =- 3 4. x = 2 5. none of these Explanation: Since f ( x ) is defined for all values of x on (- 6 , 6), the only values of x in (- 6 , 6) at which the function f is discontinuous are those for which lim x x f ( x ) 6 = f ( x ) or lim x x- f ( x ) 6 = lim x x + f ( x ) . The only possible candidates here are x =- 3 and x = 2. But at x =- 3 f (- 3) = 9 6 = lim x - 3 f ( x ) = 2 , while at x = 2 lim x 2- f ( x ) = 6 6 = lim x 2+ f ( x ) = 0 . Consequently, on (- 6 , 6) the function f fails to be continuous only at at x =- 3 , 2 . keywords: Stewart5e, 003 (part 1 of 1) 10 points If f and g are continuous functions such that lim x 5 [5 f ( x )- g ( x )] = 3 , f (5) = 2 , find the value of g (5). 1. g (5) = 2 2. g (5) = 10 3. g (5) = 13 4. g (5) = 7 correct 5. g (5) = 3 Explanation: Since f and g are continuous functions, lim x 5 (5 f ( x )- g ( x )) = 5 lim x 5 f ( x )- lim x 5 g ( x ) = 5 f (5)- g (5) = 10- g (5) ....
View Full Document

Page1 / 13

M408K Hm. 4 Solutions - Mahon, Kevin Homework 4 Due: Sep 22...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online