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Prove thefollowing inequalities. (i) 1+x^(2) gt (x sin x + cos x) " for " x in [0,oo) (ii) sin x- sin 2x le 2x """forall" x in [0, (pi)/(3)] (iii) (x^(2))/(2)+ 2x+3 le (3-x)e^(x) """for all" x le 0 (iv) 0 le x sin x-(sin^(2)x)/(2) le (1)/(2) (pi -1) " for " 0 le x le (pi)/( 2)

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