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12. Find the first and second derivatives of f (x) at x = 1.2 and x=2.0 from the following table 1.2 1.4 1.0 1.6 1.8 2.0 x f(x) 2.7183 3.3201 4.0552 4.9530 6.0496 7.3891 These values are obtained from the function y=e, Use this function to estimate the errors in the dy d'y values of and at x = 1.2 and 2.0. dx dx² Ans. f'(1.2)=3.3202, f'(2)=7.3896 f"(1.2) 3.3212, f"(2)=7.3854

12. Find the first and second derivatives of f (x) at x = 1.2 and x=2.0 from the following table 1.2 1.4 1.0 1.6 1.8 2.0 x f(x) 2.7183 3.3201 4.0552 4.9530 6.0496 7.3891 These values are obtained from the function y=e, Use this function to estimate the errors in the dy d'y values of and at x = 1.2 and 2.0. dx dx² Ans. f'(1.2)=3.3202, f'(2)=7.3896 f"(1.2) 3.3212, f"(2)=7.3854

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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12. Find the first and second derivatives of f(x) at x = 1.2 and x=2.0 from the following table 1.2 1.4 x 1.0 1.6 1.8 2.0 f(x) 2.7183 3.3201 4.0552 4.9530 6.0496 7.3891 These values are obtained from the function y=e, Use this function to estimate the errors in the dy d'y values of and at x = 1.2 and 2.0. dx dx² Ans. f'(1.2)=3.3202, f'(2)=7.3896 f"(1.2)=3.3212, f(2)=7.3854 13. The following table provides values of the function f(x)=1+ cos²x. Use interpolation to estimate the values of f'(1.32) and f"(1.65). X: 1.3 1.4 1.5 1.6 1.7 f(x): 1.071556 1.028889 1.005004 1.000853 1.016601 Ans. f'(1.32) = -0.480808, f"(1.65) = 1.975196.
Transcribed Image Text:12. Find the first and second derivatives of f(x) at x = 1.2 and x=2.0 from the following table 1.2 1.4 x 1.0 1.6 1.8 2.0 f(x) 2.7183 3.3201 4.0552 4.9530 6.0496 7.3891 These values are obtained from the function y=e, Use this function to estimate the errors in the dy d'y values of and at x = 1.2 and 2.0. dx dx² Ans. f'(1.2)=3.3202, f'(2)=7.3896 f"(1.2)=3.3212, f(2)=7.3854 13. The following table provides values of the function f(x)=1+ cos²x. Use interpolation to estimate the values of f'(1.32) and f"(1.65). X: 1.3 1.4 1.5 1.6 1.7 f(x): 1.071556 1.028889 1.005004 1.000853 1.016601 Ans. f'(1.32) = -0.480808, f"(1.65) = 1.975196.
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