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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
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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**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.
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. \(\frac{(x - 21)(x - 31)(x - 41)}{(11 - 21)(11 - 31)(11 - 41)}\)
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. \(\frac{(x - 21)(x - 31)(x - 41)}{(11 - 21)(11 - 31)(11 - 41)}\)
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