IMG_20210516_15...9.jpg )=0.5, find y(0.4) using Taylor's series 1. Given dy = y 1? +1. t 10.11. and dt expansion (3 terms) a. 0.5 b. 1.1520 C. 1.2111 d. 1.21518 e. None 2. Letf (* )= * find the Lagrange quadratic interpolation polynomial P2(x ) coefficients using the points Xo = 0. X = 1 and x2 =2. Express the polynomial in the standard form P(x) = a + ax + ax? a. ao = 0. a = -1. az = 5 b. a -0. a, = 3, az = -2 c. ao = 0, a, = -2. az = 3 d. a = 0, a = 4, ay = 3 None e. a. 3. given the following data x = [0, 0.15, 0.31, 0.5, 0.6.0.75] and 1 = [1.1.004. 1.031. 1.117. 1.223. 1.422]. the estimated value of f(04) using least square 2nd degree polynomial is: 1.0646 b. 1.0918 c. 1.0850 d. 1.0514 e. None 4. using an initial interval [8.8), the bisection method for the equation (x - 1)(x - 3)(x - 5Xx - 10)x - 12) = 0 will find the root equals to: a. 1 b. 3 c. 5 d. 10 e. None 5 using 5. What is the approximation of the root for the polynomial x? - 2x Newton's method? If we take xo =0 then x, will be: a. -1.5672 b. -2.5 c. 2.5 d. 1.5672 e. None 6. using the compound trapezoidal rule with 4 intervals to estimate the integral x dx result in: 0 a. 6.4000 b. 6.4167 c. 6.9733 d. 7.0625 e. None . . arrange these matrices 4 5 6 1 2 2 1 1 1 7. Given that A = B = C 7 8 10 2 3 3 0 0 2 in descending order according to their magnitudes. a. B. A then C b. A. B then C c. A. C then B d. B. C then A e. None Given the divided difference table, solve questions 8, 9 and 10 i X; F(xi) F111 F121 F131 F14 0 2 -7 2 0.625 0.1042 0.0078 1 4 -3 4.5 1.25 0.1667 2 6 6 9.5 2.25 3 8 25 18.5 4 10 62 8. for xo = 2, X, = 4 and x2 = 6, develop the second order Newton's polynomial to find f(4.5) a. -2 b. -1.2188 c. 3.625 d. -1.4141 e. None