For me basic maths ends with (3.1^2 - 3^2)/0.1 = (9.61-9)/0.1 = 0.61/0.1 = 6.1 (3.01^2 - 3^2)/0.01 = (9.0601-9)/0.01 = 0.0601/0.01 = 6.01 (3.001^

For me basic maths ends with (3.1^2 - 3^2)/0.1 = (9.61-9)/0.1 = 0.61/0.1 = 6.1 (3.01^2 - 3^2)/0.01 = (9.0601-9)/0.01 = 0.0601/0.01 = 6.01 (3.001^2 - 3^2)/0.001 = (9.006001-9)/0.001 = 0.006001/0.001 = 6.001 When you get to that point you are ready to start calculus and see that d/dx x^2 = 2x and that the derivative of x squared at 3 is 6. There is a smooth transition from arithmetic to calculus with the laws of calculus having to be what they are or else approximations, such as delta-x = 0.001 are not going to approximate them.