Computer Oriented Numerical Methods (BCA) 3rd Sem Previous Year Solved Question Paper 2022

Newton's Backward Difference Formula, we can work with the given data and the differences between successive values. The formula for Newton's Backward Difference is:

f(x)=f(x0​)+(x−x0​)Δf(x0​)+(x−x0​)(x−x1​)Δ2f(x0​,x1​)+…

Given data:

f(x):​11​28​314​415​54​65​76​819​

First, we need to construct a backward difference table. The differences can be calculated as follows:

Now, we can use the backward difference formula:

f(7.5)=f(7)+(7.5−7)Δf(7)+(7.5−7)(7.5−6)Δ2f(7)+(7.5−7)(7.5−6)(7.5−5)Δ3f(7)+(7.5−7)(7.5−6)(7.5−5)(7.5−4)Δ4f(7)+(7.5−7)(7.5−6)(7.5−5)(7.5−4)(7.5−3)Δ5f(7)

Now, substitute the values from the backward difference table: f(7.5)=6+0.5(4)+0.5(0.5)(13)+0.5(0.5)(0.5)(4)+0.5(0.5)(0.5)(0.5)(7)

Now, calculate the values:

f(7.5)=6+2+1.625+0.5+0.4375

f(7.5)=10.5625

So, f(7.5)≈10.5625.