PUSAT PENGAJIAN PENDIDIKAN JARAK JAUH UNIVERSITI SAINS MALAYSIA JIM 105 â BASIC MATHEMATICS

PUSAT PENGAJIAN PENDIDIKAN JARAK JAUH
UNIVERSITI SAINS MALAYSIA

SESSION 2014/2015
JIM 105 â 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.

oooOooo –