(Solved): Qi: a) Frem the given table compute the value of \( \sin 38 \) using Newten's ...

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Qi: a) Frem the given table compute the value of \( \sin 38 \) using Newten's divided difference inferpolation. (6marks) b) Consider the data \( (0,0),(0,5, a),(1,3),(2,2) \), then use the suitahic Lagrange polynomial to find \( a \), if the coefficient of \( x^{\prime} \) in the polymemial is 6 . (S marks) e) Solve \( \frac{d y}{d x}-2 x+3 y, 3(0)=1 \) by Euler's method for \( y(0.1) \). \( y(0.2) \) (s marks) d) The height of a child is measured at different ages as follows. Table: Height of the child at different ages. Estimate the height of the child as an adolt of 30 years of age using the growth nodci. \( (6 \) marks) \[ I I=\frac{a}{I+l \mathrm{c}^{+a}} \] Q4: The velocity v of particle trasels distances from a point on its path is given by the table. a) Estimate the time taken to tmvel 60 meter by using Simpson's one third value. b) Compare the result with Simpson's \( 3 / 8 \) rule. (8 marks)