Question

Find the equation of the curve passing through the (0,1), (1,3), (3,1) and (4,0) using the Lagrange polynomial

Answer 1

I Solution. We know that :- " Lagranges enterpolating polynomial. Here the lagranges interpolating poly can be worn as linear combination. Pulx) = loa) fo + dels of + de la fet – – – + halos fun (es. where li n-no) (n-ni). – ... & -ki-1) Craviti)... (rynx) (24-70) (_jxo) - (x; -Mj-1)... (4-3)

A/c question giver data in xol11 314 fim 1 131 10 Now, from given data lo - (x-x)(x-x2)(x-23) (20-x) (no-22) (no-2) (2-1) (1) (2-3) (2-4) (-3) (-4) In-no (non (n-13) (24-26) (2,-2) (2, -1) ( -o) (x-3)(n-4) (1) (-2) (-3) I l I (W7x² + 12x) -70² + 12x) 0 (0-20) (-34) (n-xz) (-20) (22-24) (2-3) (-o) (2-1) (x-4) (3-0) (3-1) (3-4)

e Az = (1-xo) (upah) (n-u) (ng-ho) (-2) (x3-24) (81-0) (2-1) (81-3) (4-0) (4-1) (4-3) (les at (x2-14 x² + 3x)) using the value of lo, le, de we get and lz in egr 0, By data ! to=1 t=3 t2=1 L 13-0 P(x) = -1 (x²8x² + 190-12).(1 +7 (23 70² +12%)(3) 9-52+uw). (1 + (x?4x2+3^)(0) P(x) = - 1 (² 8x²+19x-12)+1 3 ² 21x²+362-23 +522 - 4 Pow) - (13–84+192-12) ++ [23° -46x +32 33 Plno = " **+83–192 +12 +432-32x2+643] Pod - 1/2 [ 328_24x²+ 45 x +12]] @ ie I Pa) = (x² – 2x² + 45 x + 1 Therefore, this is required lagranges polynomial by given daba