(3) Z (i) By sketching a suitable pair of graphs, show that the equation Inx=2-x²¹ has only one root. (ii) Verify by cal

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3 Z I By Sketching A Suitable Pair Of Graphs Show That The Equation Inx 2 X Has Only One Root Ii Verify By Cal 1 (23.85 KiB) Viewed 26 times

(3) Z (i) By sketching a suitable pair of graphs, show that the equation Inx=2-x²¹ has only one root. (ii) Verify by calculation that this root lies between x = 1.3 and x = 1.4. (iii) Show that, if a sequence of values given by the iterative formula X = √(2-In.x₂) [1] converges, then it converges to the root of the equation in part (i). (iv) Use the iterative formula x = √(2-In.x) to determine the root correct to 2 decimal places. [3] Give the result of each iteration to 4 decimal places. (2) 121