1. (a) Evaluate the following integra 3x dr.10-7x+x2 )Let P(, y) be a general point on the quartic polynomial y = and let Q be the point(3,)as shown in the sketch below.y y=(,y)Q(3,0) (i) Write down an expression for the distance between P and Q in terms of: (ii)Show that has a critical point at the value of which satisfies the polynomial equation 4x+x-3=0: (ii) Without actually finding r, show that the solution of this equation lies in the interval [0.3: (iv)Show that (is a (global) minimum at this r value. (v)Use Newton’s method, with an initial guess of 1.5 to find an approxi- mation(accurate to two decimal places)to the solution of4x7+x-3=0 (Newton’s method for solving /()=0 In+=I.-5(x.) for n=0. 1, 2,…) ‘()
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