Unit-4

Numerical analysis

Q1) Evaluate-

A1)

We have-

Q2) Using Newton’s forward difference formula, find the sum

A2)

Putting

It   follows that

Since is  a  fourth  degree polynomial in  n.

Further,

By Newton Forward Difference Method

Q3) Given find   , by using  Newton forward  interpolation  method.

A3)

Let , then

The table of forward finite difference is given below:

By Newton forward difference method

Here initial value = 45, difference of  interval  h = 5 and  the value to be calculated at x=52.

By Formula

                                Q4) Find the missing term in the following:

A4)

Let

First we construct the forward difference table:

Now,

Q5) Find from the following table:

A5)

 Consider the backward difference method

  Here

By Newton backward difference formula

Q6) The following table give the amount of a chemical  dissolved in water:

  Compute the amount dissolve at

A6)

Consider the following backward difference table:

Here

   By  Newton  Backward  difference formula

Q7) The following are the marks obtained by 492 candidates  in a certain examination

Find out the number of candidates:

a)       Who secured more than 48  but  not more than  50 marks?

b)       Who secured less than 48  but  not  less than 45 marks?

A7)

Consider the  forward difference table given below:

     Here 

 By Newton Forward Difference formula

f

a)       No. of  candidate secured more than 48  but  not more than  50 marks

b)      No. of  candidate secured less than 48 but  not  less  than 45 marks

Q8) In the table given below, the values are consecutive terms of a series of which 23.6 is the 6th term then find out the 1st and 10th term.

A8)

The difference table will be as follows-

To find the first term, we will use Newtons’s forward interpolation formula-

With

We get,

To find the 10th term-