Differentiation and application of diffentiation

PUSAT PENGAJIAN PENDIDIKAN JARAK JAUH

UNIVERSITI SAINS MALAYSIA

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.

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.

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