# Numerical Analysis-Inverse Interpolation (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 2 of 2

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## Question number: 1

» Numerical Analysis » Inverse Interpolation

Appeared in Year: 2015

### Describe in Detail

Compute the value of by Simpson’s 1/3 ^{rd} rule. Given that ln4.0 = 1.39, ln4.2 = 1.43, ln4.4 = 1.48, ln4.6 = 1.53, ln4.8 = 1.57, ln5.0 = 1.61, ln5.2 = 1.65

### Explanation

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 = 0, 1, 2, 3, 4, 5, 6

Here, b = 5.2, a = 4, h = 0.2, f (x) = lnx

## Question number: 2

» Numerical Analysis » Inverse Interpolation

Appeared in Year: 2014

### Describe in Detail

Given the following values of the function y = f (x); evaluate f (4) and also find x for which f (x) = 25.

f (1) = 10, f (2) = 15, f (3) = 42.

### Explanation

Given that y = f (x), So

x 1 2 3 4

y 10 15 42?

To find the missing value, we use binomial expansion method. Here 3 values are known, we would take third order finite difference zero. Thus,

Second question is that if we