Assignment #2 MTH101 (Fall 2010)

[Xpert]

Maximum Marks: 25

Due Date: Nov 22, 2010
DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
• To solve this assignment, you should have good command over 11-14 lectures.

• Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in the 11 to 14 lectures.
  

• Upload assignments properly through LMS, No Assignment will be accepted
through email.
• Write your ID on the top of your solution file.

• Don’t use colorful back grounds in your solution files.
  
• Use Math Type or Equation Editor etc for mathematical symbols.
  
• You should remember that if we found the solution files of some students are same then we will reward zero marks to all those students.
  
• Try to make solution by yourself and protect your work from other students, otherwise you and the student who send same solution file as you will be given zero marks.
  
• Also remember that you are supposed to submit your assignment in Word format any other like scan images etc will not be accepted and we will give zero marks correspond to these assignments.
  

Question 1)
Use [FONT="]definition (definition 2.6.3) to prove that

[/FONT][FONT="][SIZE=12pt]Question 2:
[/SIZE][/FONT] Find the points of discontinuity of the given function
[FONT="][SIZE=12pt]
[/SIZE][/FONT]
[FONT="][SIZE=12pt]Question 3:
[/SIZE][/FONT]
Find a non-zero value for the constant “k” so that

Will be continuous at x=0
[FONT="]
Solution will be provided soon.
[/FONT]

[sweethira]

w8ing.............

[Xpert]

ok good to wait.

[sweethira]

Sigh!!!!!!!!!!!!!!!wht good to w8 ?

[Xpert]

wait na. ab itni bhi kia jaldi hai. app bhi kuch share kar dia karo

[sweethira]

hhmmmmm acha khud he kuch karti hun

[Xpert]

han aur share bhi karana ta kay kuch dusray students ka bhi faida ho jay.

[Xpert]

Idea solution check it out.
Q1. Use epsilon-delta definition to prove
Limit as x-->-3 (x^2-9)/(x+3)= -6

Ans. |x+3|<epsilon iff 0<|x+3|<delta

Q2. Find the points of discontinuity of the given function
f(x)=(x+3)/|x^2+3x|

Ans. Points of discontinuity are 0 and -3 in both the cases (when absolute sign is removed we get two cases. 1. (x^2+3x) and 2. -(x^2+3x) .. am I right??)

Q3. Find a non-zero value for the constant “k” so that

f(x)= tan(kx)/x if x<0
3x+2k^2 if x>0
will be continuous at x=0

Ans. k=1/2

Note: Please donot consider this answers 100% true as there may be some mistake from my side (I'm not a cheetah in math ) ... anyways .. please if you find your answers different from mine .. Kindly do notify so we can discuss which answer are correct. Thank you!!

[kinga]

Question 1 and 2 are ok as i have got the same answer. How you solved the third question please share the method

[IQ-test]

oh dear you can do it by your self. you from where?