# Numerical Analysis-Interpolation Formulae [ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)]: Questions 7 - 13 of 14

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## Question number: 7

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

Appeared in Year: 2011

### Describe in Detail

Use Simpson’s rule with five ordinates to compute an approximation to π with the help of the integration of the function (1 + x ^{2}) ^{-1} from 0 to 1.

### Explanation

T he rule of the integrand using Simpson’s rule for five ordinates is

where , n = 5

h= (1 - 0) /5 = 1/5

We divide the range 0 to 1 in five equal part i. e.

… (157 more words) …

## Question number: 8

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

Appeared in Year: 2012

### Describe in Detail

An unknown function u _{x} has been tabulated below for some selected values of x. Use Newton’s divided difference formula on these to find an approximate value of u _{3}:

x | 0 | 2 | 5 | 10 |

u | 3 | 19 | 73 | 223 |

### Explanation

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## Question number: 9

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2012

### Describe in Detail

Solve the equation f (x) = 0 by using a suitable interpolation formula on the following values:

x | 3 | 4 | 5 | 6 |

f (x) | -2.8 | -1.2 | -0.3 | 1.8 |

### Explanation

To solve the equation f (x) = 0, using Lagrange’s inverse interpolation method

… (203 more words) …

## Question number: 10

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2015

### Describe in Detail

Fit the exponential curve y = a + bx to the following data

x: 0 2 4

y: 5.01 10 31.62

### Explanation

his is not exponential equation, it is a straight line y = a + bx

S. no | x | y | Xy | x |

1 | 0 | 5.01 | 0 | 0 |

2 | 2 | 10 | 20 | 4 |

3 | 4 | 31.62 | 126.48 | 16 |

Sum | 6 | 46.63 | 146.48 | 20 |

The normal equations is

Using the table, putting these values in normal equations. We get

Solving these two equations, we get the value of

… (24 more words) …

## Question number: 11

» Numerical Analysis » Interpolation Formulae » Newton-Gregory

Appeared in Year: 2010

### Describe in Detail

Evaluate log _{e} 7 by Simpson’s -1/3rd rule.

### Explanation

We get log _{e} 7, when

So, the seven ordinates of the integrand using Simpson’s rule is

Where h = 1/6 (b-a) and y _{k} =f (a + kh) for k = 1,2, 3,4, 5,6, 7

Here, b = 7, a = 1, h = 1, f (x) =

… (67 more words) …

## Question number: 12

» Numerical Analysis » Interpolation Formulae » Newton-Gregory

Appeared in Year: 2010

### Describe in Detail

Estimate U _{2} from the following table:

x | 1 | 2 | 3 | 4 | 5 |

U | 7 | - | 13 | 21 | 37 |

### Explanation

To find the missing value, we use binomial expansion method. Here 4 values are known, we would take fourth order finite difference zero. Thus,

Here for x = 1, U _{0} =7, U _{1} =? , U _{2} =13, U _{3} =21, U _{4} =37

## Question number: 13

» Numerical Analysis » Interpolation Formulae » Gauss

Appeared in Year: 2009

### Describe in Detail

Find the value of

by taking 5 subintervals and using the Trapezoidal rule.

### Explanation

Let

First divided the interval into 5 subintervals

x | 0 | 1/4 | 1/2 | 3/4 | 1 |

y | 1 | 16/17 | 4/5 | 16/25 | ½ |

Here a = 0, b = 1, n = 4, h= (b-a) /n = 1/4

the Trapezoidal rule is

… (1 more words) …