Prove that Δ∇ = Δ – ∇ - Business Mathematics and Statistics

Prove that Δ∇ = Δ – ∇

Sum

L.H.S = Δ∇

= (E – 1)(1 – E^–1)

= E – EE^–¹ + E^–¹

= E – 1 – 1 – E^–¹

= E – 2 – E^–¹ .........(1)

R.H.S = Δ – ∇

= (E – 1) – (1 – E^–¹)

= E – 1 – 1 + E^–¹

= E – 2 + E^–¹ ........(2)

From (1) and (2)

L.H.S = 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. ii) | Page 121

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 f(x) = x² + 3x than show that Δf(x) = 2x + 4

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