University:
Swansea University
Course:
MA-252 | Probability Theory
Academic year:

2023
Views:

494

Pages:

7
Author:

Amal J.

Q. Using Lagrange's formula, the find value the of polynomicalPn (x) and also find x forwhich polynomial is data. maximum or minimumfor the following x3no x2I2 8xy4yo (2 5yrs/y2 4 yyy(x) = (x-xi) (x-x2) (x-x3) go(xo-x2) (xo. - x3)+ (x-no) (x-xx) (x-x3) y,(x4-xo) (x1- n2) (x,-xB)+ (x-no) (x-xi) (x-x3) y2(x2-xo) (x2. - x1) xx2-x3)to (x-xo) (x-xi) (x-x2) Y3(x3-xo)= (x-2) (x-7) (x-8)4(1-2) (1-7) UCO 61-8)+ (x-1) (a-7) (x-8) 5(2-1) (2-7) (2-8) (x-8) 5(7-1) (7-2) (7-8)+ (x-1) (x-2) (x-7)4(8-1) (8-2) (8-7)y(x)(x-2) (x-7) (x-8) 10.00 42 6215 Janes-42.200 is+ (x-1) (x.-17)306 &+ (x-) (x-2)(x-8)of (Exc-)r) 30-6 (15-x)+ (XLD) (x-2) (x-7) or A 2c) (4.42 21st -Un)(sir= (x-2) to(E St) (ix 2d) COKESet Class - (x-8)( 01 - 86+(x4-1) (x-2) (.2-8)-6(@-1)(Q-2) 11 08 - 1C 8 - 2)21 ) (11 -5 - = (49-92+14)(2-8) X2-21from+ (n°-8x+7) (x-8)ur 6- xx816+ (no-8x+7) (x-2) x221xs.)= - Q - -pss21+6+24x-tax-162-6 -+ (x) 8/n° +16x+72-14) Peppl=+ 18x3 21 DFC - of 2(9x4 2 - -21+ - To 8n° +64x+7x-566+ 3x - -24x - -2x-166++ (-2n2 +16x +7x-14)2 -21 Perp18x2 = 144x - 28x-22421+40x+5x-401-614x9 - 126xx+ 19652921- 406 1 - 92+14] - 5x°+40 x t5x - 402T3=2xi-18x+28 -36= 4x. - 36x +56y(x)6.77=19-93-166.For maximum or minimumf(x) = O.f(x) 16P'cx). t -2x+9] = 0-2x+9 =0S-2x-9n n=9/2 = 4.5 olsUsing Lagrange's formula of interpolationfind f(d.5).given. tox1 N2 x3n78 10x6y19:31d9ylayor y(9.5) = (9.5-"$) (9.5-9) -(9.5-10) 3(7-8) (7-9) (7-10)dup(9.5-9) (9.5-10)(8-7) up (8-9) (8-10)+ (9.5-7) (9.5-8) (9.5-10managini (9-7) (9+8) (9-10)()+(10-7.).(10-8) (10-9)gPHXS=- 1.125+1-1-64 0.625Zepthe - 1,875 + 216.875-26 = 0.1875 + -0.3125 + 0.9375+ 2.8125 RV= 3.625