ELT J solve the Dirichlet Problem on the rectangle [014] × [0₁3] Uxx +llyy =0, 04×44, 024≤3 U(0,y) = U(4,4)=0,0² 423 11(210) = 0₁ 11(x43) = 100 04X24 04444
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- 1/1 100 NINN 23) -4V192X 25) -4V216x'y-zIf y=u³-4 and u = 3x² + 10, find y' O 18x(3x² + 10)² O 3x(6x² + 10)² 18(3x² + 10)² O 6x(3x² +10)² Moving6. Differentiate: y = A. x²+1 x²+3x-1 -x²+1 (x²+3x-1)² x² + 3x - 1 2x²+3 aldetin-(x²+1) B. D. (x²+3x-1)² x²-1 x²+3x-1 xls 101 S= 8 Xllstat XS = (x)"}_0 D (o
- 9, (xD- 3xD+41)j=0 condition JW=3.6, )=0.4SP. E=2*10^5 I=30000 L=600 W=25 y = dy dx = W 120EIL 3 - x² +21²³x²³ - 1+x) W 2-₁²) 120EIL ( = 5x² + 6(³X²-(+) IV assume as р P = = 5x² + 62²x² - L^=0 Using MATLAB, Solve x from P(x)= 0 using Bisection method between a=100 and b=300 (3% allowable error) Put the obtained value of x to get value of y3 17) pla) = a' - 5; Find p(x - 4)
- The top and bottom margms Op a poster are are 8 cm and Hhe Side mary Ms'are each 6 cm if Hhe ae a of pante ol material on the paster is hikeb, 6at 386 cm² And the dimension's of the poster with the Smallest area 386=XY A = (X+816)CY t 2) १९८ । 386 y=386 386+ 12) メ A=X+16)7 8cm A=X·386 X. 386x %3D 22.686 192 386+12x+ 6176 4 日ミax+G176X+578 A 12-6176X 12-6176X*2 =o.-6176 7- 12 -2 176 ax x.1な GI76 ズ 12x² 12x2= 6176 %3D 519.66=VX Ca2.686=X) 12 x²-514.66 %3D 386 17.01:7 22.686 1-11) P(x) = x² - 6x³ +14x² - 54x + 45 aun no benewens woy noltsmotni ert s2U (s) (ga) 3+xT-E- ²x + x = (x) 9 (01 of menoont sulav otsibsmotal er: ezu (d) 20 2.1-bns 2 S-nsewted 0193 6 21 919rls worde và têExE + x = (x) ai (edning >) 11a) possible positive rational zeros:_ 11a) possible negative rational zeros:_ 11b) list of possible rational zeros:_ 11c) rational zeros:_ complex zeros: 11d) factored form: P(x) =6) yỳ = ỳ(ỳ + 2)