Numerical Analysis Questions and Answers – Gauss’s Forward Interpolation Formula

This set of Numerical Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Gauss’s Forward Interpolation Formula”.

1. What will be the solution for the following table using Gauss’s forward interpolation formula, where x = 3?

x f(x)
1 1
2 1
3 1

a) 1
b) 0.328
c) 0.327
d) 0.322
View Answer

Answer: a
Explanation:
Gauss's forward method to find solution
h=2-1=1
The central difference table is

x p=(x-2)/1 y Δy
1 -1 1
0
2 0 1
0
3 1 1

Solution of Gauss's forward interpolation is y(3)=1.

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2. What will be the solution for the following table using Gauss’s forward interpolation formula, where x = 2?

x f(x)
1 2
2 3
3 4

a) 0.2452
b) 0.2864
c) 0.2862
d) 3
View Answer

Answer: d
Explanation:
Gauss's forward method to find solution
h=2-1=1
Now the central difference table is

x p=(x-2)/1 y Δy Δ2y
1 -1 2
1
2 0 3 0
1
3 1 4
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Solution of Gauss's forward interpolation is y(2)=3.

3. What will be the solution for the following table using Gauss’s forward interpolation formula, where x = 1?

x f(x)
1 2
2 3
3 4
4 8
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a) 11.152
b) 2
c) 11.122
d) 11.128
View Answer

Answer: b
Explanation: Given,
Gauss's forward method to find solution
h=2-1=1
Now the central difference table is

x p=(x-2)/1 y Δy Δ2y Δ3y
1 -1 2
1
2 0 3 0
1 3
3 1 4 3
4
4 2 8

Solution of Gauss's forward interpolation is y(1)=2.

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4. What will be the solution for the following table using Gauss’s forward interpolation formula, where x = 2.5?

x f(x)
1 2
2 6
3 4
4 8
5 10
6 12

a) 1
b) 4.1774
c) 4.1797
d) 2
View Answer

Answer: c
Explanation:
Gauss's forward method to find solution
h=2-1=1
Now the central difference table is

x p=(x-3)/1 y Δy Δ2y Δ3y Δ4y Δ5y
1 -2 2
4
2 -1 6 -6
-2 12
3 0 4 6 -20
4 -8 30
4 1 8 -2 10
2 2
5 2 10 0
2
6 3 12

Solution of Gauss's forward interpolation is y(2.5)=4.1797.

5. What will be the solution for the following table using Gauss’s forward interpolation formula, where x = 4?

x f(x)
1 2
2 6
3 4
4 8
5 10
6 12
7 24
8 26
9 28

a) 8
b) 9
c) 7
d) 6
View Answer

Answer: a
Explanation:
Gauss's forward method to find solution
h=2-1=1
Now the central difference table is

x p=(x-5)/1 y Δy Δ2y Δ3y Δ4y Δ5y Δ6y Δ7y Δ8y
1 -4 2
4
2 -3 6 -6
-2 12
3 -2 4 6 -20
4 -8 30
4 -1 8 -2 10 -32
2 2 -2 -4
5 0 10 0 8 -36 138
2 10 -38 134
6 1 12 10 -30 98
12 -20 60
7 2 24 -10 30
2 10
8 3 26 0
2
9 4 28

Solution of Gauss's forward interpolation is y(4)=8.

6. What will be the solution of the equation 4x+1 using Gauss’s forward interpolation formula where x1
= 2 and x2 = 4 and x = 2.1, step value (h) = 0.25?
a) 8.4
b) 9.4
c) 8
d) 5
View Answer

Answer: b
Explanation:
Gauss's forward method to find solution
h=2.25-2=0.25
Now the central difference table is

x p=(x-3)/0.25 y Δy Δ2y
2 -4 9
1
2.25 -3 10 0
1
2.5 -2 11 0
1
2.75 -1 12 0
1
3 0 13 0
1
3.25 1 14 0
1
3.5 2 15 0
1
3.75 3 16 0
1
4 4 17

Solution of Gauss's forward interpolation is y(2.1)=9.4.

7. What will be the solution of the equation 2x 2 using Gauss’s forward interpolation formula, where x1 = 1 and x2 = 2 & x = 2 & step value (h) = 0.25?
a) 2
b) 7
c) 5
d) 8
View Answer

Answer: d
Explanation:
Gauss's forward method to find solution
h=1.25-1=0.25

Now the central difference table is

x p=(x-1.5)/0.25 y Δy Δ2y Δ3y
1 -2 2
1.125
1.25 -1 3.125 0.25
1.375 0
1.5 0 4.5 0.25
1.625 0
1.75 1 6.125 0.25
1.875
2 2 8

Solution of Gauss's forward interpolation is y(2)=8.

8. What will be the solution of the equation 3x using Gauss’s forward interpolation formula, where x1 =
2 and x2 = 4 & x = 2 & step value (h) = 0.25?
a) 8
b) 6
c) 5
d) 1
View Answer

Answer: b
Explanation:
Gauss's forward method to find solution
h=2.25-2=0.25
Now the central difference table is

X p=(x-3)/0.25 y Δy Δ2y
2 -4 6
0.75
2.25 -3 6.75 0
0.75
2.5 -2 7.5 0
0.75
2.75 -1 8.25 0
0.75
3 0 9 0
0.75
3.25 1 9.75 0
0.75
3.5 2 10.5 0
0.75
3.75 3 11.25 0
0.75
4 4 12

Solution of Gauss's forward interpolation is y(2)=6.

9. What will be the solution of the equation x + 1 using Gauss’s forward interpolation formula, where x1 = 1 and x2 = 2 & x = 1 & step value (h) = 0.25?
a) 1
b) 3
c) 2
d) 4
View Answer

Answer: c
Explanation:
Gauss's forward method to find solution
h=1.25-1=0.25
Now the central difference table is

X p=(x-1.5)/0.25 y Δy Δ2y
1 -2 2
0.25
1.25 -1 2.25 0
0.25
1.5 0 2.5 0
0.25
1.75 1 2.75 0
0.25
2 2 3

Solution of Gauss's forward interpolation is y(1)=2.

10. What will be the solution of the equation x using Gauss’s forward interpolation formula, where x1 = 1 and x2 = 2 & x = 1 & step value (h) = 0.25?
a) 4
b) 2
c) 3
d) 1
View Answer

Answer: d
Explanation:
Gauss's forward method to find solution
h=1.25-1=0.25
Now the central difference table is

X p=(x-1.5)/0.25 y Δy Δ2y
1 -2 1
0.25
1.25 -1 1.25 0
0.25
1.5 0 1.5 0
0.25
1.75 1 1.75 0
0.25
2 2 2

Solution of Gauss's forward interpolation is y(1)=1.

11. What will be the solution of the equation sin(x) using Gauss’s forward interpolation formula, where x1 = 1 and x2 = 2 & x = 1 & step value (h) = 0.25?
a) 4
b) 2
c) 3
d) 0.0167
View Answer

Answer: d

Explanation:
Gauss's forward method to find solution
h=1.25-1=0.25
Now the central difference table is

X p=(x-1.5)/0.25 y Δy Δ2y Δ3y Δ4y
1 -2 0.8415
0.1075
1.25 -1 0.949 -0.059
0.0485 -0.003
1.5 0 0.9975 -0.062 0.0039
-0.0135 0.0008
1.75 1 0.984 -0.0612
-0.0747
2 2 0.9093

Solution of Gauss's forward interpolation is y()=0.0167.

12. What will be the solution of the equation cos(x) using Gauss’s forward interpolation formula, where x1 = 1 and x2 = 2 & x = 1 & step value (h) = 0.25?
a) 0.9496
b) 2
c) 3
d) 0.0167
View Answer

Answer: a
Explanation:
Gauss's forward method to find solution

h=1.25-1=0.25
Now the central difference table is

X p=(x-1.5)/0.25 y Δy Δ2y Δ3y Δ4y
1 -2 0.5403
-0.225
1.25 -1 0.3153 -0.0196
-0.2446 0.0152
1.5 0 0.0707 -0.0044 0.0003
-0.249 0.0155
1.75 1 -0.1782 0.0111
-0.2379
2 2 -0.4161

Solution of Gauss's forward interpolation is y()=0.9496.

13. What will be the solution of the equation tan(x) using Gauss’s forward interpolation formula, where x1 = 1 and x2 = 2 & x = 1 & step value (h) = 0.25?
a) 0.9496
b) 4190.0569
c) 3
d) 0.0167
View Answer

Answer: b
Explanation:
Gauss's forward method to find solution
h=1.25-1=0.25

Now the central difference table is

X p=(x-1.5)/0.25 y Δy Δ2y Δ3y Δ4y
1 -2 1.5574
1.4522
1.25 -1 3.0096 9.6397
11.0919 -40.3533
1.5 0 14.1014 -30.7137 94.0241
-19.6218 53.6708
1.75 1 -5.5204 22.9571
3.3353
2 2 -2.185

Solution of Gauss's forward interpolation is y()=4190.0569.

14. What will be the solution of the equation cot(x) using Gauss’s forward interpolation formula, where x1 = 1 and x2 = 2 & x = 1 & step value (h) = 0.25?
a) 0.9496
b) 4190.0569
c) 3.3389
d) 0.0167
View Answer

Answer: c
Explanation:
Gauss's forward method to find solution
h=1.25-1=0.25
Now the central difference table is

X p=(x-1.5)/0.25 y Δy Δ2y Δ3y Δ4y
1 -2 0.6421
-0.3098
1.25 -1 0.3323 0.0485
-0.2614 -0.0392
1.5 0 0.0709 0.0093 0.0054
-0.2521 -0.0337
1.75 1 -0.1811 -0.0244
-0.2765
2 2 -0.4577

Solution of Gauss's forward interpolation is y()=3.3389.

15. What will be the solution of the equation sec(x) using Gauss’s forward interpolation formula, where x1 = 1 and x2 = 2 & x = 1 & step value (h) = 0.25?
a) 4191.0168
b) 4190.0569
c) 3.3389
d) 0.0167
View Answer

Answer: a
Explanation:
Gauss's forward method to find solution
h=1.25-1=0.25
Now the central difference table is

X p=(x-1.5)/0.25 y Δy Δ2y Δ3y Δ4y
1 -2 1.8508
1.3205
1.25 -1 3.1714 9.6449
10.9655 -40.3575
1.5 0 14.1368 -30.7125 94.0243
-19.7471 53.6668
1.75 1 -5.6102 22.9543
3.2072
2 2 -2.403

Solution of Gauss's forward interpolation is y()=4191.0168.

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