Allied maths:CAT 2 MCQ

Estimate f(1.5) using Lagrange interpolation.

• −0.8673

• -0.7214

• −0.9773

• -0.9113

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

• 25

• 21

• 23

• 32

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

• 3.826

• 3.2567

• 3.2113

• 3.912

• 3.125

• 3.327

• 3.542

• 3.837

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

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

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

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

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

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

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

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

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

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

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

• Linear

• Quadratic

• Cubic

• Quartic

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

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

The methods to find the polynomials approximation are ..

• Lagrange interpolation

• Newton's Divided Difference

• Natural Cubic Spline

• Clamped Cubic Spline