Prove that (1 + Δ)(1 – ∇) = 1

Sum

L.H.S = (1 + Δ)(1 – ∇)

= (E)(E^–1)

= E^1–1

= E°

= 1

= R.H.S

Hence proved.

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Finite Differences

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Chapter 5: Numerical Methods - Miscellaneous problems [Page 121]

Chapter 5 Numerical Methods
Miscellaneous problems | Q 2. i) | Page 121

Evaluate Δ(log ax)

If y = x³ – x² + x – 1 calculate the values of y for x = 0, 1, 2, 3, 4, 5 and form the forward differences table

If h = 1 then prove that (E^–1Δ)x³ = 3x² – 3x + 1

Find the missing entry in the following table

x	0	1	2	3	4
y_x	1	3	9	-	81

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