2. (i) By sketching y = cos x and y = x³ – 1 on the same coordinate system, show that f(x) = cos x – - x³ +1 = 0 in some interval. (ii) Using part (i), find the interval where the root lies. (iii) Use bisection method to find an approximate value of the solution f (x) = 0 in the interval found in part (ii).

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.