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How do you make a Trial and Improvement question?

How do you make a Trial and Improvement question?

Ok so i get how you answer trial and improvement questions but how do you make a trial and improvement question? I need this. Please show me an example because I really don't understand. Please can someone explain to me because i want to learn how to make a question. Thanks!

Consider the area of a curved line say f(x) = x^2 form x = 1 to x = 10 bounded also by the x axis.

You can approximate this are by drawing a rectangle with the base of c = 1 to 10 (9 units) and the height of f(1).

To refine the approximation, cut the base in half and use the height of two rectangles as f(1)*4.5 + f(4.5)*4.5 = 1*4.5 + 22.5*4.5

This is called a refinement or as you called it an “improvement”

Continue dividing the base in smaller and smaller sections and use the value of the function of the left side of the interval to get the height of the rectangle. Continue until the area of these rectangles do not change much (your choice of “much”

Good luck.

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