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
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7134eb63-d3bd-40e7-b2fe-88ddb22a3ee9%2Fd08896a3-12e8-4609-bf78-cf6f27772afd%2Ftvx80ht_processed.jpeg&w=3840&q=75)
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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