Following are the population of a district Year (x) 1881 1891 1901 1911 1921 1931 Population (y)Thousands 363 391 421 - 467 501 Find the population of the year 1911

Following are the population of a district

Year (x)	1881	1891	1901	1911	1921	1931
Population (y) Thousands	363	391	421	-	467	501

Find the population of the year 1911

योग

Since only five values of fix) are given, the polynomial which fits the data is of degree four.

Hence fifth differences are zeros.

i.e. Δ⁵y₀ = 0

(E – 1)⁵y₀ = 0

(E⁵ – 5E⁴ + 10E³ – 10E² + 5E – 1)y₀ = 0

E⁵y₀ – 5E⁴y₀ + 10E³y₀ – 10E²y₀ + 5Ey₀ – y₀ = 0

y₅ – 5y₄ + 10y₃ – 10y₂ + 5y₁ – y₀ = 0

501 – 5(467) + 10(y₃) – 10(421) + 5(391) – 363 = 0

2456 – 6908 + 10y₃ = 0

– 4452 + 10y₃ = 0

⇒ 10y₃ = 4452

y = `4452/10` = 445.2

The population of the year 1911 is 445.2 thousands

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Finite Differences

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अध्याय 5: Numerical Methods - Exercise 5.1 [पृष्ठ ११२]

अध्याय 5 Numerical Methods
Exercise 5.1 | Q 7 | पृष्ठ ११२

Evaluate Δ(log ax)

Evaluate Δ`[1/((x + 1)(x + 2))]` by taking ‘1’ as the interval of differencing

Find the missing entries from the following.

x	0	1	2	3	4	5
y = f(x)	0	-	8	15	-	35