Holistic Numerical Methods Institute

committed to bringing numerical methods to undergraduates

Multiple Choice Test

Newton's Divided Difference Method

Q1. If a polynomial of degree n has more than n zeros, then the polynomial is

oscillatory
zero everywhere
not defined

Q2. The following x-y data is given

 x 15 18 22 y 24 37 25

The Newton’s divided difference second order polynomial for the above data is given by

f2(x)=b0+b1(x-15)+b2(x-15)(x-22)

The value of b1 is

-1.048

0.1433
4.333
24.00

Q3. The polynomial that passes through the following x-y data

 x 18 22 24 y ? 25 123

is given by

The corresponding polynomial using Newton’s divided difference polynomial is given by

f2(x)=b0+b1(x-18)+b2(x-18)(x-22)

The value of b2 is

0.2500
8.125
24.00
not obtainable with the information given

Q4. Velocity vs. time data for a body is approximated by a second order Newton’s divided difference polynomial as

The acceleration in m/s2 at is

0.5540 m/s2

39.622 m/s2
36.852 m/s2
not obtainable with the given information

Q5. The path that a robot is following on a x-y plane is found by interpolating the following four data points

 x 2 45 5.5 7 y 7.5 7.5 6 5

The length of the path from x=2 to x=7 is

Q6. The following data of the velocity of a body is given as a function of time.

 Time (s) 0 15 18 22 24 Velocity (m/s) 22 24 37 25 123

If you were going to use quadratic interpolation to find the value of the velocity at seconds, the three data points of time you would choose for interpolation are

0, 15, 18
15, 18, 22
0, 15, 22
0, 18, 24

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