1.14. Use the binomial approximation (1.58) (Problem 1.12) to evaluate (1 10-20) 1. Can you evalu-...

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1.14. Use the binomial approximation (1.58) (Problem 1.12) to evaluate (1 10-20) 1. Can you evalu- ate this directly on your calculator? - 1.12. In the discussion of the Michelson-Morley experi- ment, we twice used the binomial approximation (1 − x) ~ 1 - nx (1.58) which holds for any number n and any x much small- er than 1 (that is, x << 1). (In the examples, n was -1 and -2, and x = 32 was of order 10-8.) The binomial approximation is frequently useful in relativity, where one often encounters expressions of the form (1-x)" with x small. Make a table show- ing (1-x)" and its approximation 1 - nx for n = -and x = 0.5, 0.1, 0.01, and 0.001. In each case find the percentage by which the approximation differs from the exact result. " 1.14. Use the binomial approximation (1.58) (Problem 1.12) to evaluate (1 10-20) 1. Can you evalu- ate this directly on your calculator? - 1.12. In the discussion of the Michelson-Morley experi- ment, we twice used the binomial approximation (1 − x) ~ 1 - nx (1.58) which holds for any number n and any x much small- er than 1 (that is, x << 1). (In the examples, n was -1 and -2, and x = 32 was of order 10-8.) The binomial approximation is frequently useful in relativity, where one often encounters expressions of the form (1-x)" with x small. Make a table show- ing (1-x)" and its approximation 1 - nx for n = -and x = 0.5, 0.1, 0.01, and 0.001. In each case find the percentage by which the approximation differs from the exact result. "

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