To determine To calculate: To determine a best estimate for the depth (in meters) at which the temperature is 10-degree centigrade. Explanation Given information: Temperature at 9-meter depth = 8-degree C and the temperature at 5- meter depth = 15-degree C. Calculation: Let x be the depth in meters and the function f ( x ) be the temperature of water at corresponding depth. From the given data we have f ( 9 ) = 8 ∘ and f ( 5 ) = 15 ∘ . Now we use the secant method to estimate the depth at which the temperature is 10 degrees. Write the formula for the secant method. x i + 1 = x i − f ( x i ) ( x i − x i − 1 ) f ( x i ) − f ( x i − 1 ) Now we need to estimate the value of x for which f ( x ) = 40 . f ( x ) = 10 ⇒ f ( x ) − 10 = 0 Let the function f ( x ) − 10 be g ( x ) and apply the secant method to this function with the initial guesses x 0 = 5 and x 1 = 9

3rd Edition

ISBN: 9780134696454

Author: Sauer, Tim

Publisher: Pearson,

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Chapter 1.5, Problem 4E

To determine

To calculate:To determine a best estimate for the depth (in meters) at which the temperature is 10-degree centigrade.

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Chapter 1.5, Problem 3E

Chapter 1.5, Problem 5E

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