Pre-Calc Homework Solutions 453

Step 1 x n c holds for n 1 3 3 x x 3 3 3 because k

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Unformatted text preview: i c. Then c (i 1) c. 4. Step 1: x ( 1) 1 3 Step 2: Suppose c i 1 3.41 x 0.41; thus x 1 1 i c k 1 The mathematical induction principle now guarantees the original formula for every positive integer n. 12. Step 1: The formula holds for n number x), because x1 xk 1 Step 2: From the graph, 0.77, or 9 25 1 (and every real 1 0.36. 16 7 9 9 16 9 0.36; thus 25 25 1 x1 k x. x k Step 2: Suppose x x . Then xk x xk x x k 1. k xk x The mathematical induction principle now guarantees the original formula for every positive integer n (and every real number x). 5. Step 1: (2x 2) ( 6) 0.02 2x 4 0.02 0.02 2x 4 0.02 4.02 2x 3.98 2.01 x 1.99 Step 2: x ( 2) x 2 2 x 2 0.01. 6. Step 1: x 1 1 0.1 0.1 0.9 x 1 1.1 0.81 0.19 x 0.21 Step 2: x 0 x x 1 1 0.1 x 1 1.21 0.19....
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