Construct the Lagrange interpolating polynomial L3(x) = yolo(x) + yılı(x) + yzl2(x) + yzl3(x), for the function given in the table \(x\) \(11\) \(21\) \(31\) \(41\) \(2\) \(3\) \(y\) \(5\) \(6\) The polynomial l1(x) is
Construct the Lagrange interpolating polynomial L3(x) = yolo(x) + yılı(x) + yzl2(x) + yzl3(x), for the function given in the table \(x\) \(11\) \(21\) \(31\) \(41\) \(2\) \(3\) \(y\) \(5\) \(6\) The polynomial l1(x) is
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:**The polynomial \( l_1(x) \) is**
Select one:
- **a.** \(\frac{(x - 21)(x - 31)(x - 41)}{(11 - 21)(11 - 31)(11 - 41)}\)
- **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.** \(\frac{(x - 11)(x - 21)(x - 31)}{(41 - 11)(41 - 21)(41 - 31)}\)
This section presents a multiple-choice question, asking the user to identify the correct polynomial expression for \( l_1(x) \). Each option provides a polynomial expression with variables and constants organized in a factored rational form.
![(There are 5 questions connected with this problem. Please keep your calculations.)
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
\[
\begin{array}{cccc}
x & 11 & 21 & 31 & 41 \\
y & 2 & 3 & 5 & 6 \\
\end{array}
\]
The polynomial \( l_1(x) \) is
Select one:
○ a. \(\frac{(x - 21)(x - 31)(x - 41)}{(11 - 21)(11 - 31)(11 - 41)}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F215c9956-76b8-4988-9874-46d947288784%2F43939a38-234e-447f-8edf-3dcbf08bb973%2Fedrx4ko_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(There are 5 questions connected with this problem. Please keep your calculations.)
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
\[
\begin{array}{cccc}
x & 11 & 21 & 31 & 41 \\
y & 2 & 3 & 5 & 6 \\
\end{array}
\]
The polynomial \( l_1(x) \) is
Select one:
○ a. \(\frac{(x - 21)(x - 31)(x - 41)}{(11 - 21)(11 - 31)(11 - 41)}\)
Expert Solution
Step 1
Legranges interpolation
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
