Q1 When proving that what is the maximum value of when

Using Definition 2.3.2


Hence =0.00599 is the maximum value .

Q2. Prove using -definition ?

Using difference between two squares gives since . Thus the value of

Q3.Evaluate the following limits if they exist. But if they do not exist, give reasons.

a. =1/4

b. =-1


d. =5

Q4. If for some real number , prove that

Squeezing theorem

Q5. Using Intermediate value theorem show that the equation has a solution between 1 and 2?

Since f(1)=- while f(2)=+


  1. Find =4
  2. Find =1

  3. Is there a value of c which makes f(x) continuous ?