{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

assignment 3 answers

assignment 3 answers - Section 2.4 Page 1 Section 2.5 Page...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Page 1 Section 2.4
Image of page 1

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

View Full Document Right Arrow Icon
Page 1 Section 2.5
Image of page 2
Page 2 Section 2.5
Image of page 3

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

View Full Document Right Arrow Icon
Page 1 Section 2.6
Image of page 4
Math 151 - D100 Fall 2010, Solutions to instructor problems HW3 A.1 For which a, b R is the function f ( x ) = 1 - x - 1 ax if x (0 , 1] 1 if x = 0 bx 4 + bx x 2 + x if x ( - 1 , 0) continuous on ( - 1 , 1]? Using the theorems in section 2.5 of the textbook that state: 1) that rational func- tions are continuous everywhere on their domain, 2) that root functions are con- tinuous at every number in their domain, and 3) that the sum of two continuous functions is continuous, we can state that: 1. 1 - x - 1 ax is continuous on (0 , 1] 2. bx 4 + bx x 2 + x is continuous on ( - 1 , 0) It remains to be shown then that f ( x ) is continuous at x = 0. By the definition of continuity, for f ( x ) to be continuous at x = 0, we must have that lim x 0 of f ( x ) = f (0). f (0) = 1 by the definition of f ( x ). Therefore, the limit of f ( x ) as x approaches 0 must be 1. This in turn means that both the left hand and right hand limit of f ( x ) as x approaches 0 must be 1. The statement about the left hand limit means that lim x 0 - bx 4 + bx x 2 + x = 1 or lim x 0 - bx ( x 3 + 1) x ( x + 1) = lim x 0 - b ( x 3 + 1) ( x + 1) = 1 Therefore
Image of page 5

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

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern