# Quiz Chapter 05.04: Lagrangian Interpolation

 MULTIPLE CHOICE TEST LAGRANGIAN INTERPOLATION INTERPOLATION

1. Given $n + 1$ data pairs, a unique polynomial of degree _____ passes through the $n + 1$ data points.

2. Given the two points $\left[ a,f(a) \right], \left[ b, f (b) \right]$, the linear Lagrange polynomial $f_{1}(x)$ that passes through these two points is given by

3. The Lagrange polynomial that passes through three data points given by

 $x$ $15$ $18$ $22$ $y$ $24$ $37$ $25$
• $f_{2} \left( x \right) = L_{0}(x) \left( 24 \right) + L_{1}(x) \left( 37 \right) + L_{2}(x) \left( 25 \right)$

The value of $L_{1}(x)$ at $x = 16$ is

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

 Time (s) $10$ $15$ $18$ $22$ $24$ Velocity (m/s) $22$ $24$ $37$ $25$ $123$

A quadratic Lagrange interpolant is found using three data points, $t=15, \, 18,$ and $22$. From this information, at what of the times given in seconds is the velocity of the body $26$ m/s during the time interval of $t = 15$ to $22$ seconds.

5. The path that a robot is following on an $x - y$ plane is found by interpolating four data points as

 $x$ $2$ $45$ $5.5$ $7$ $y$ $7.5$ $7.5$ $6$ $5$
• $y \left( x \right) = 0.15238x^{3} - 2.2571x^{2} + 9.6048x - 3.9000$

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

6. 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 $t = 14.9$ seconds, what three data points of time would you choose for interpolation?