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Easiest Ways to solve limit and continuity

Easiest Ways to solve limit and continuity

05/05/2021
Easiest Ways to solve limits of every function (with example)
Edubomb Edubomb

Do you think you are weak in the limit problem? do you hate mathematics? I'm sharing here, easiest ways to solve every limit problem. Maybe you have zero concepts in the limit, But you can boost your speed in solving limit-related problems by just following some techniques provided here. Just remember THREE BASIC TYPES OF PROBLEM-SOLVING STRATEGY.

1.Type I problem (factorization)

2.Type II problem (rationalization)

3.Type III problem (Formula)

 

FUNDAMENTAL FORMULA TO REMEMBER

 

YOU CAN ADD EACH LIMIT VALUES SEPARATELY

 

YOU CAN MULTIPLY EACH LIMIT VALUES SEPARATELY

 

YOU CAN DIVIDE  EACH LIMIT VALUES SEPARATELY

 

CONSTANT ARE TAKEN OUTSIDE OF LIMIT 

 

 

DERIVED FORMULA TO REMEMBER

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Steps for calculation of the limit 

1. First of all build concept of limit. Click here for the basic concept (Basic concept of limit in mathematics)

2. Remember indeterminant form of limit which are 0/0∞/∞-, 0×∞,1 , etc. 

3. Analyse the types of problems before solving them.  does it solve by factorizing, rationalizing, or using formula?

4. solve each problem step by step until you get the final answers.

 

 

SOLVED EXAMPLE

Example-evaluate the following limit

Type I problem (factorization)
  1.      b)       c)

Solutions:

A.    

 When put   then given function yield   which is indeterminant form.

  

 

 

 

 

B.  

When we put x=2  then given function yield  which is indeterminant form

 

      

   

 

C. 

 

 

 

 

 

 

Type II problem (rationalization)
  1.    b)  

          c)

Solution:

A. When we put value of x=∞ then above function yield ∞-∞ which is indeterminant form.

 

   

        

        

      

         

 

B.   

When we put x=0  then the above function yield  form which is indeterminant form.

 

 

 

 

 

 

 

C. 

 

   

 

 

 

Type III problem (formula)

A. 

 

 

 

After cancelling (x-2) we get

 

 we get

 

 

 

B. Evaluate

Put x-2=y  so that when x2  then y0

 

 

 

Applying formula   we get

 

 

 

C.   

Solution:

 

 

Applying formula    we get

 

 

EXERCISE

1. what is the limit of a given function?

2. what are the best ways to remember the types of problems involve in solving the limits of given functions?

3. what are indeterminant forms? what does mean them?

4. Evaluate

5. Evaluate  

6.Evaluate

7. Evaluate  

8. Evaluate

MCQs (Answer are encircled)

1. Limiting values of  

 0

 1

 5

2

2. limiting value of       

 +1/2

 4

 -1/2

 -4

3. limit of  

 2

 6

 3

1

4. Limit of    

1

-4

4

1

5. limit of  

 3

 6

 4

 0

6. which if the following is not indeterminant form?

 0/0

  0

 0×∞

 ∞-

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