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) 
(b) 
2. Evaluate
(a) 
(b) 
3. Given 
Is f continuous at x = 5 ? Explain why?
4. Let 
By using the definition of derivatives i.e.
if limit exists, find 
.
5. Find if
(a) 
(b) 
6. Find 
if
(a) 
(b) 
7. Find a third-degree polynomial of the form 
such that
8. Find the equation of the tangent line to the circle 
at the point 
9. Use linear approximation to estimate 
.
10. Determine where the function 
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.
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.
- Evaluate
(a)
(b)
- Evaluate
(a)
(b)
- Given
Is f continuous at x = 5 ? Explain why?
- Let By using the definition of derivatives i.e. if limit exists, find .
- Find if
(a)
(b)
- Find if
(a)
(b)
- Find a third-degree polynomial of the form such that
- Find the equation of the tangent line to the circle at the point
- Use linear approximation to estimate .
- Determine where the function 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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