All calculus students know that the derivative of a function / at x can be defined as fl, , .. fix + h) - f{x) f (x) = hm . h-*0 h Choose your favorite function /, nonzero number x, and computer or calculator. Generate approximations f'n(x) to fix) by fix + 10-") -fix) /.w = ^ for rt = 1,2,... ,20, and describe what happens.

Test 1 Study Guide Here is a list of topics to be familiar with for the test, and some practice problems. Note: when studying/working on these problems, how you solve each problem is just as important as the solution; you must show your work on the test. No calculators, but you won’t need them. The emphasis of the test will be on chapter 1, but you will still be expected to be comfortable with the properties of absolute values and inequalities from chapter 0 and the examples of functions we went over in chapter 2. - 0.1/2 arithmetic of real numbers; identities like the di▯erence of two squares - 0.3 intervals (open, closed, half-open), set notation, equations and inequalities involving absolute values. 1. Find all numbers x that satisfy the equation j2x ▯ 5j =