Math 1A - Fall 1998 - Bergman - Midterm 2

Math 1A - Fall 1998 - Bergman - Midterm 2 - WED 17:33 FAX...

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: 10/03/2001 WED 17:33 FAX 6434330 MOFFITT LIBRARY I001 George M. Bergman Fall 1998, Math 1AW 6 November, 1998 2050 VLSB Second Midterm 3: 10—4:00 PM 1. (50 points, 10 points apiece) Find the following. 2x” ex+1 (a) llmxal 16—1 1— cos 2x 03) llmeO 1 u-cos 3x' (c) An antiderivative of the function x + x_1 (d) A function satisfying the differential equation f ’(x) = ~—9 f(x), and such that f (1) - f(0) = 1 7 i cosh x (6) dx 1 + x 2. (25 points) (a) (10 points) State the principle of mathematical induction. (b) (15 points) Suppose f is an infinitely differentiable function (i.e., a function such that f ’, f ”, , fol), all exist). Prove that for all positive integers 11, one has D" (x f(x)) : xf(n)(x) + nf("_1)-(x). Here fan means f. Suggestion: Use mathematical induction. x2+1 5 3. (25 points) (a) (15 points) Give the information asked for below about the curve y = in If any of the items asked for does not exist, write “None”. (For limits, write “None” only if the function does not approach either a real number or i co.) (b) (10 points) Sketch the curve._ Your sketch does not need to reflect accurate numerical values of the coordinates of the various transition points, as long as it correctly shows the order in which these occur. x—intercept(s): y—intercept: increasing on interval(s): decreasing on interval(s): concave up on interval(s): concave down on interval(s): vertical asymptote(s): 11m hmx __>_oo y = _ extrema: 36—)on = ...
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