0182016992

kklee@kkleemaths.com

GET STARTED

Tuition Timetable

Check the latest timetable of my tuition classes.

Private Tuition

Contact me at 018-2016992 for more info.

Resources

Complete Resources about past year questions are here.

Ai Tuition

Visit Ai Tuition Website for more subjects tuition.

VIEW ALL SERVICES

Back to Blog

Read Article

Discussion – 

4

Read Article

Discussion – 

4

STPM PBS Assignment

STPM 2016 Mathematics (T) Term 2 Assignment

By KK LEE

February 25, 2016

Introduction

The concept of a limit plays a central role in calculus. For example, continuity, derivative and integral require this concept. In this assignment, you are required to explore the concept of a limit.

Sample Question

Question 1

(a) Draw an equilateral triangle inscribed in a circle of radius  x cm. Express the area of the triangle A_3 in term of x.

(b) Repeat 1(a) with square, regular pentagon, regular hexagon, …, regular polygon with n sides in the circle of radius x cm.

(c) Determine the value of \frac{A_n}{x^2} correct to three decimal places when n is large.

Question 2

A function  f_k  is defined by  f_k(x) =(1+kx)^{\frac{1}{x}}.

(a)(i) Tabulate the values x and f_1(x) when x equals to 0.1, 0.01, 0.001, …. Deduce value of \lim_{x\to 0} f_1(x).

(a)(ii) Tabulate the values x and  f_k(x) for k = 2, 3 and 4, when x equals to 0.1, 0.01, 0.001, ….  Deduce value of  \lim_{x\to 0}f_k(x).

(b) Show that \lim_{x\to\infty} \left(1+\frac{k}{x}\right)^x=\lim_{x\to 0}(1+kx)^\frac{1}{x}.

Question 3

A function g is defined by g(t) = \int_1^t \frac{1}{x(x+1)}dx, where t>1.

(a) Suppose t is an integer, estimate g(t) using the trapezium rule with

(i) t-1 strips,

(ii) 2(t-1) strips,

(iii) 4(t-1) strips.

In each case, express g(t) in terms of  t and determine $\lim_{t\to\infty} g(t)$.

(b) Suppose t is a real number, find g(t) using integration and determine $\lim_{t\to\infty} g(t)$.

(c) Comment on your findings.

 

 

 

Sample Solution
Sample solution will not be posted for this semester. Assignment sample solution will be continued only after this semester.

Sorry. Please discuss with your friends or teacher to get more information of the coursework. And thanks for viewing this website.

Dear my students, please join the my Facebook Group to get the full solution for Question 3 (a) (iii).

Click here to know the reason
Comment

Comment Link

Join KK LEE STPM Mathematics Facebook Group

Dear my students

Join the group to view all the extra solutions

Join Now

Here are our most recent updates posts

- Feel free to check it out -

Tags: Integration limits MT Term 2 STPM 2016 STPM MT

KK LEE

KK LEE has been a STPM Mathematics tuition teacher since June 2006, but his love of Maths dates back to at least 1999 when he was Form 4. KK LEE started teaching in 2006 at Pusat Tuisyen Kasturi. He was known as "LK" when he was teaching in PTK. After teaching STPM Mathematics for 8 years in PTK, he joined Ai Tuition Centre in 2014. Over the years he has taught Mathematics (T), Mathematics (S), Mathematics (M), Additional Mathematics.

4 Comments

  1. ashley
    ashley on April 8, 2016 at 9:04 pm

    Sir! Thank you for guiding us all these semesters!!! I’ve learned a lot from your solutions!
    Sir, I do really appreciate your hard work! THANK YOU SIR!!

    Reply
    • KK LEE
      KK LEE on April 9, 2016 at 9:06 am

      Thanks

  2. jack
    jack on June 5, 2016 at 7:24 pm

    sir can you post the sample answer already? sem 2 already over , i need it as reference . Thank you in advance

    Reply
    • jack
      jack on June 5, 2016 at 7:27 pm

      oh , if sir do not wish to post it yet then can you email me the sample answer , i really need it ,thanks!

Submit a Comment

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

You May Also Like

No Results Found

The page you requested could not be found. Try refining your search, or use the navigation above to locate the post.