PUSAT PENGAJIAN PENDIDIKAN JARAK JAUH UNIVERSITI SAINS MALAYSIA JIM 105 – BASIC MATHEMATICS

    PUSAT PENGAJIAN PENDIDIKAN JARAK JAUH
    UNIVERSITI SAINS MALAYSIA

    ACADEMIC
    SESSION 2014/2015
    JIM 105 – BASIC MATHEMATICS

    Assignment 1

    This assignment
    covers topics on limit and continuity, differentiation and application of diffentiation. It should be done collaboratively in a group
    consisting of 5 students. The names and IC number of each group member
    should be written/printed on the front cover of the assignment. Answer all questions and the assignment must
    be hand written. The due date for
    submission of Assignment 1 is 31st December 2014.

    1. Evaluate
    (a) .gif”>

    (b) .gif”>

    2. Evaluate
    (a) .gif”>

    (b) .gif”>

    3. Given .gif”>
    Is f continuous
    at x =
    5 ? Explain why?

    4. Let .gif”> By using the
    definition of derivatives i.e..gif”> if limit exists, find .gif”>.

    5. Find .gif”> if
    (a) .gif”>
    (b) .gif”>

    6. Find .gif”> if
    (a) .gif”>

    (b) .gif”>

    7. Find a third-degree polynomial of the form
    .gif”> such that
    .gif”> .gif”>

    8. Find the equation of the tangent line to
    the circle .gif”> at the point .gif”>

    9. Use linear approximation to estimate .gif”>.

    10. Determine where the function .gif”> is increasing and
    decreasing and where its graph is concave up and concave down. Find the relative extrema and inflection
    points (if exist) and sketch the graph of
    f.


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