Question

using difference table find the value of (Δ)2y given the values of (x, y) as (1,5),(2,14),(3,21)?​

Answer 1

Answer:

Using difference table find the value of (Δ)2y given the values of (x, y) as (1,5),(2,14),(3,21)?. Add answer. Log in to add comment.

Answer 2

Δ²y value is -2.

Given,

x  = 1, 2, 3.

y = 5, 14, 21

To Find,

Δ²y.

Solution,

Here, the values for x given are 1, 2, and 3.

And values for y are 5, 14, and 21.

Using the difference table we need to find out the value of Δ²y.

From the given values,

x₀ = 1

x₁ = 2

x₂ = 3.

y₀ = 5.

y₁ = 14.

y₂ = 21.

next, find out whether the values are equispaced or not.

For that,

x₁ - x₀ = 2 - 1

1.

x₂ - x₁ = 3 - 2

1.

So, the points are equispaced.

To find the first forward difference value Δy,

Δyₙ  = yₙ⁺₁  - yₙ.

Δy₀ = Δy₁ - Δy₀

Δy₀ = y₁ - y₀

Δy₀ = 14-5

Δy₀ = 9.

Δy₁ = y₂-y₁

Δy₁ = 21 - 14

7.

In the question, we need to find out the value of the second forward difference, Δ²y.

Δ²yₙ = Δyₙ⁺₁ - Δyₙ.

Δ²y₀ = Δy₁ - Δy₀

Δ²y₀ = 7 - 9

Δ²y₀ = -2.

Hence, -2 is the value of Δ²y.

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