hw1a 475 - ECON475 HW#1 Answers 1 the sequence 1 Theorem...

Info icon This preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: ECON475 HW #1 Answers 1. , the sequence 1 Theorem 5.1 As . Furthermore, lim converges to a limit denoted by the symbol 1 . Proof Let / 1/ , 1 ; so . As lim 1 1 gets larger and goes to infinity, so does lim . Letting . (r is fixed.) Since . 1 1 , we find lim 1 1 2. In 1960; 5-year plan of Turkey indicated that per capita real income of Turkey will double in 20 years. i) What should be average growth rate of per capita real income for that? 1 2 20 ln 1 ln 2 3,52% 3. If , show that 3 We know that the derivative of f is (at point . ): Then, lim lim lim 3 3 lim 3 . 3 3 lim 4. Does Differentiability Continuity hold? No! i) (Differentiability Continuity) Proof Let : be differentiable at lim . Then, the limit exists and is the same for every sequence which converges to 0. If a function is differentiable at every point in its domain D, we say that the function is differentiable. 1 is continuous at if lim . Let lim . If f is differentiable, then at lim , lim 0 lim .0 0 exists. Let us now consider continuity. If lim that is continuous. lim Since lim , then we can say lim Therefore, ii) is differentiable, both limits exist. Thus, lim is continuous. (Continuity , 0, i.e. lim ) | |. Note that f is continuous everywhere, but it is not does not exist. 1 1 0 . 0 Consider : differentiable at 0 lim Why? 0 2 ...
View Full 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