# MTH603 Quiz 2 Solution and Discussion

• Given the following data x:1 2 5 y:1 4 10 Value of 1st order divided difference f[2 , 5] is

• Given the following data x:4 5 7 10 y:46 102 294 346 Value of 1st order divided difference f[5 , 7] is

91
92
94
96

• Forthegivendatapoints(x0,y0),(x1y1),(x2y2),and(x3,y3)thezero−orderdividedifferencewillbegivenas

• Forthegivendatapoints(4,45),(5,104),and(6,190),thezero−orderdividedifferencewillbe

• For the following data

• Whichofthefollowingmethodcanbeusedforinterpolationforthegivenvaluesofxandy?x y0.30.0670.70.2480.90.518

Lagrangens interpolation

• If y(x) is approximated by a polynomial Pn(x) of degree n then the error is given by

ε(x)=y(x)+Pn(x)
ε(x)=y(x)−Pn(x)
ε(x)=y(x)×Pn(x)
ε(x)=y(x)÷Pn(x)

• Forthegivendividedifferencetablex 1 4 7y2.23.54.11stD.D0.43330.22ndD.D−0.0389theNewton′sdividedifferenceinterpolationformulawillbe

y=f(x)=2.2+(x−1)(−0.0389)+(x−1)((x−4)(0.4333)

y=f(x)=2.2+(x−1)(0.4333)+(x−1)((x−4)(−0.0389)

y=f(x)=−0.0389+(x−1)(0.4333)+(x−1)((x−4)(2.2)

y=f(x)=−0.0389+(x−1)(2.2)+(x−1)((x−4)(0.4333)

Solution:

• Forthegivendividedifferencetablex 1 4 7y2.23.54.11stD.D0.43330.22ndD.D−0.0389theNewton′sdividedifferenceinterpolationformulawillbe

y=f(x)=2.2+(x−1)(−0.0389)+(x−1)((x−4)(0.4333)

y=f(x)=2.2+(x−1)(0.4333)+(x−1)((x−4)(−0.0389)

y=f(x)=−0.0389+(x−1)(0.4333)+(x−1)((x−4)(2.2)

y=f(x)=−0.0389+(x−1)(2.2)+(x−1)((x−4)(0.4333)

• Whatwillbethevalueof′a′inthegivendividedifferencetable? x2468y0.51.11.72…21stD.D0.30.30.252ndD.Da−0.01253rdD.D−0.0021

• For the given data points (1,0.3),(3,1),and(5,1.2) the divide difference table will be given as

Forthegivendatapoints(1,0.3),(3,1),and(5,1.2)thedividedifferencetablewillbegivenas

• For the given data points (1,0.3),(3,1),and(5,1.2) the divide difference table will be given as

• Δ=----- ?

E−1/2
1-E
E-1
None

• Δ=----- ?

• In Lagrange’s interpolation, for the given five points we can represent the function f (x) by a polynomial of degree

3
4
5
6

• In Simpson’s 1/3 rule, the global error is of ………………

O(h2)
O(h3)
O(h4)
None of the given choices

5

2

1

1

4

65

1

4
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