GATE 2024 CE (CE1) – Question 32
Consider the data of $f(x)$ given in the table.
| $i$ | 0 | 1 | 2 |
|---|---|---|---|
| $x_i$ | 1 | 2 | 3 |
| $f(x_i)$ | 0 | 0.3010 | 0.4771 |
The value of $f(1.5)$ estimated using second-order Newton's interpolation formula is ______________ (rounded off to 2 decimal places).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.16 to 0.18
Explanation
The divided differences are $f[x_0, x_1] = \frac{0.3010 - 0}{1} = 0.3010$, $f[x_1, x_2] = \frac{0.4771 - 0.3010}{1} = 0.1761$ and $f[x_0, x_1, x_2] = \frac{0.1761 - 0.3010}{2} = -0.06245$. Newton's formula gives $f(1.5) = 0 + 0.3010(1.5 - 1) - 0.06245(1.5 - 1)(1.5 - 2) = 0.1505 + 0.01561 = 0.1661 \approx 0.17$.