Free Printable Numerical Interpolation

1.

Estimate f(1.5) using Lagrange interpolation.

a)

−0.8673

b)

-0.7214

c)

−0.9773

d)

-0.9113

2.

Find f(2) for the data f(0) = 1, f(1) = 3 and f(3) = 55 using Newton's divided difference formula.

a)

25

b)

21

c)

23

d)

32

3.

Find f(0.25) using Newton's divided difference formula

a)

3.826

b)

3.2567

c)

3.2113

d)

3.912

4.

a)

3.125

b)

3.327

c)

3.542

d)

3.837

5.

Given the two points $\left(a,f\left(a\right)\right),\left(b,f\left(b\right)\right)$ , the linear Lagrange polynomial $f1\left(x\right)$ that passes through these two points is given by

a)

$f1\left(x\right)=\frac{x-b}{a-b}f\left(a\right)+\frac{x-a}{a-b}f\left(b\right)$

b)

$f1\left(x\right)=\frac{x}{b-a}f\left(a\right)+\frac{x}{b-a}f\left(b\right)$

c)

$f1\left(x\right)=f\left(a\right)+\frac{f\left(b\right)-f\left(a\right)}{b-a}\left(b-a\right)$

d)

$f1\left(x\right)=\frac{x-b}{a-b}f\left(a\right)+\frac{x-a}{b-a}f\left(b\right)$

6.

As you were provided with 3 data points, which formula you can use in the next step?

a)

$P_2\left(x\right)\ =L_o\ f_o+L_1\ f_1$

b)

$P_3\left(x\right)\ =L_o\ f_o+L_1\ f_1$

c)

$P_2\left(x\right)\ =L_o\ f_o+L_1\ f_1+L_2\ f_2$

d)

$P_3\left(x\right)\ =L_o\ f_o+L_1\ f_1+L_2\ f_2$

7.

Based on the data given, which is the suitable type of polynomial to do the approximation?

a)

Linear

b)

Quadratic

c)

Cubic

d)

Quartic

8.

What is the value of $L_o\ f_o$ ? Please provide the answer in 2 decimal points.

(a)

9.

What is the value of $L_1\ f_1$ ? Please provide the answer in 2 decimal points.

(a)

10.

The methods to find the polynomials approximation are ..

a)

Lagrange interpolation

b)

Newton's Divided Difference

c)

Natural Cubic Spline

d)

Clamped Cubic Spline

11.

(1+ $\Delta$ ) (1+ $\nabla$ ) =

a)

0

b)

1

c)

2

d)

3

12.

$\Delta\nabla$

a)

$\nabla-\Delta$

b)

$\Delta-\nabla$

c)

$\Delta+\nabla$

d)

none

13.

$\nabla=$

a)

E $\nabla$

b)

$E^{-1}\Delta$

c)

$E^{-1}\nabla$

d)

$E\Delta$

14.

f(x)-f(x-h)=

a)

$\Delta f\left(x\right)$

b)

$\nabla f\left(x\right)$

c)

E(x)

d)

none

15.

(E-1)/E

a)

$\Delta$

b)

$\nabla$

c)

$\Delta\nabla$

d)

none

16.

E[E(y₀)] =

a)

y₀

b)

Y₁

c)

Y₂

d)

Y

17.

$If\ k\ is\ constat\ then\ \ \Delta k\ is$

a)

k

b)

1

c)

0

d)

$\nabla k$

18.

Backward difference operator pronounced as

a)

delta

b)

lamda

c)

nabla

d)

alpha

19.

$If\ h=1\ then\ \Delta\left(x^2\right)=$

a)

2x

b)

2x-1

c)

2x+1

d)

1

20.

E(f(x))=

a)

f(x-h)

b)

f(x)

c)

f(x+h)

d)

f(x+2h)

21.

What is the value of z?

a)

6

b)

-6

c)

-36

d)

4

22.

What is an appropriate first row command to solve this by Gaussian Elimination?

a)

2R2 + R2 -> R2

b)

-2R1 + R2 -> R2

c)

R3 +R2 --> R3

d)

2R1 + R2 --> R2

23.

Which row command is an appropriate next step?

a)

7R2 + R3 -> R3

b)

-7R1 + R3 -> R3

c)

7R3 -> R3

d)

-7R2 + R3 -> R3

24.

$\Delta=$

a)

$E-1$

b)

$E+1$

c)

$e-1$

d)

None of these

25.

$\delta=$

a)

$\frac{1}{2}\left(E^{\frac{1}{2}}-E^{-\frac{1}{2}}\right)$

b)

$\frac{1}{2}\left(E^{\frac{1}{2}}+E^{-\frac{1}{2}}\right)$

c)

$\frac{1}{2}\left(E^{-\frac{1}{2}}-E^{\frac{1}{2}}\right)$

d)

$\frac{h}{2}\left(E^{-\frac{1}{2}}-E^{\frac{1}{2}}\right)$

26.

$\mu=$

a)

$\frac{1}{2}\left(E^{\frac{1}{2}}+E^{-\frac{1}{2}}\right)$

b)

$\frac{1}{2}\left(E^{\frac{1}{2}}-E^{-\frac{1}{2}}\right)$

27.

$E^{-2}f\left(x\right)=$

a)

$f\left(x-2h\right)$

b)

$f\left(x-2h\right)-f\left(x\right)$

c)

$f\left(x+2h\right)$

d)

$f^{-2}\left(x\right)$

28.

$\Delta^2y_0=$

a)

$\Delta y_1-\Delta y_0$

b)

$\Delta y_0-\Delta y_1$

c)

$\Delta^2y_1-\Delta^2y_0$

d)

$\Delta y_1+\Delta y_0$

29.

∆2^x=…………….

a)

2^(x+h)-2^x

b)

2^(x+h)

c)

2^(x-h)-2^x

d)

2^(x-h)

30.

$If\ f\left(x\right)=a_0x^n+a_1x^{n-1}+...+a_{n-1}x+a_n,\ \ a_0\ne0,\ then\ \Delta^nf\left(x\right)=$

a)

$a_0h^n$

b)

$n!h^n$

c)

$a_0n!h^n$

d)

$n!$

Numerical Interpolation

Total questions: 30

Worksheet time: 2hrs 27mins

Similar Resources on Wayground