Ki o 1,3|2,3|3.3 3,7 n,1 4,5 5 2 14,1 158 183 21,5 24;7 294 32 According to the table above given calaulate this integral guD approxinate with minimu (X) erro B) g'(23)+g(3,7) calaulate the deritative value approximately using the centrol difference formula

G Lt A={1, 3, 5} B= 2.7,9, 7 R =1 (1,2), 13, 7) ,13, 11) , (S,1 RIA B not funclion %3D show 9: IR 1R dekined by gc) = 3 x²+5 x +2 voR Rind the domain ofR tet Show that 3 is funclion and O ut f: Q Qgiven lay f(f)= P+9 where P, 9 E7 and 1+0 find the domain of R Punelion. and Show that f. not he IR IR olefined by xe IR 2x -5 hca) = x' +3 then 2X -S A x 70 Im h= x' +3 X CO

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Tef (x,XXn) be n iudependeut random sampte from f Size n from auniform" dritribution e lutenal (9 Find the Cidif f eo, te minimam order sfatic ( 6 fend tee Cid if of Xend, te makimm order Stetistic C) Find tee mean end Varianee f XG and (Xn

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If F = F,I+ Fj +F;k then prove that div F %3D ду

Find the valueof the consraut (min) that makes the DaE f X dx -Cyf~*) dy so CHomogeneous, exect, separable aud Linear)

The vertical distance covered by a rocket from -8 to t-30 seconds is given by 140000 x-ו ) 2000In -9.8tdt 140000 2100t a) Find the distance covered from t= 10 to 25 seconds Use the two-segment trapezoidal rule b) Use four segment Simpson's 1/3rd Rule to estimate x. For part b, design an EXCEL spreadsheet that the estimates x for n-2, 4, and 6.

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(0.3470, 2.9404) y = 2 + cos(x) 2- (2.2962, 1.3365) y = csc(x) -1 2 Let R be the region bound by the equations y = 2 + cos(x) and y = csc(x) in the first quadrant on the interval 0sx<7. a) Write, but do not solve, an equation involving integral expressions whose solution is the area of the region R. b) Write, but do not solve, an equation involving integral expressions whose solution is the volume of the solid generated when R is revolved around the x-axis. c) Write, but do not solve, an equation involving integral expressions whose solution is the volume of the solid generated when R is revolved around the line x = -1. 3. 1.