your calculations.) Construct the Lagrange interpolating polynomial L3(x) = yolo(x) + yılı (x) + y2l2(x) + y3l3(x), for the function given in the table \(æ\) \(11\) \(21\) \(y\) \(2\) \(3\) \(31\) \(41\) \(5\) \(6\) The polynomial l2(x) is Select one: O a. (x – 11)(x – 21)(x – 31) (41 – 11)(41 – 21)(41 – 31) O b.
your calculations.) Construct the Lagrange interpolating polynomial L3(x) = yolo(x) + yılı (x) + y2l2(x) + y3l3(x), for the function given in the table \(æ\) \(11\) \(21\) \(y\) \(2\) \(3\) \(31\) \(41\) \(5\) \(6\) The polynomial l2(x) is Select one: O a. (x – 11)(x – 21)(x – 31) (41 – 11)(41 – 21)(41 – 31) O b.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![## Lagrange Interpolating Polynomial
**(There are 5 questions connected with this problem. Please keep your calculations.)**
### Task
Construct the Lagrange interpolating polynomial
\[ L_3(x) = y_0 l_0(x) + y_1 l_1(x) + y_2 l_2(x) + y_3 l_3(x), \]
for the function given in the table:
\[
\begin{array}{ccccc}
x & 11 & 21 & 31 & 41 \\
y & 2 & 3 & 5 & 6 \\
\end{array}
\]
### Problem
The polynomial \( l_2(x) \) is
**Select one:**
- a. \(\frac{(x - 11)(x - 21)(x - 31)}{(41 - 11)(41 - 21)(41 - 31)}\)
- b.
- c.
(Note: Options b and c are not shown in the image.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F215c9956-76b8-4988-9874-46d947288784%2Fa90e0617-691b-406c-b88e-7ae7fee8d239%2Fdzy3qxi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Lagrange Interpolating Polynomial
**(There are 5 questions connected with this problem. Please keep your calculations.)**
### Task
Construct the Lagrange interpolating polynomial
\[ L_3(x) = y_0 l_0(x) + y_1 l_1(x) + y_2 l_2(x) + y_3 l_3(x), \]
for the function given in the table:
\[
\begin{array}{ccccc}
x & 11 & 21 & 31 & 41 \\
y & 2 & 3 & 5 & 6 \\
\end{array}
\]
### Problem
The polynomial \( l_2(x) \) is
**Select one:**
- a. \(\frac{(x - 11)(x - 21)(x - 31)}{(41 - 11)(41 - 21)(41 - 31)}\)
- b.
- c.
(Note: Options b and c are not shown in the image.)
Transcribed Image Text:The polynomial \( l_2(x) \) is
Select one:
- a. \(\frac{(x - 11)(x - 21)(x - 31)}{(41 - 11)(41 - 21)(41 - 31)}\)
- b. \(\frac{(x - 11)(x - 21)(x - 41)}{(31 - 11)(31 - 21)(31 - 41)}\)
- c. \(\frac{(x - 11)(x - 31)(x - 41)}{(21 - 11)(21 - 31)(21 - 41)}\)
- d. \(\frac{(x - 21)(x - 31)(x - 41)}{(11 - 21)(11 - 31)(11 - 41)}\)
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