In Exercises 67–73, estimate derivatives using the symmetric difference quotient (SDQ), defined as the average of the difference quotients at h and -h: 1(f(a + h) – f(a) f (a – h) – f(a) -h f (a + h) – f(a – h) | 1 2h The SDQ usually gives a better approximation to the derivative than the difference quotient. 67. The vapor pressure of water at temperature T (in kelvins) is the atmospheric pressure P at which no net evaporation takes place. Use the following table to estimate P'(T) for T = 303, 313, 323, 333, 343 by computing the SDQ given by Eq. (1) with h = 10. т (К) 293 303 313 323 333 343 353 P (atm) 0.0278 0.0482 0.0808 0.1311 0.2067 0.3173 0.4754
In Exercises 67–73, estimate derivatives using the symmetric difference quotient (SDQ), defined as the average of the difference quotients at h and -h: 1(f(a + h) – f(a) f (a – h) – f(a) -h f (a + h) – f(a – h) | 1 2h The SDQ usually gives a better approximation to the derivative than the difference quotient. 67. The vapor pressure of water at temperature T (in kelvins) is the atmospheric pressure P at which no net evaporation takes place. Use the following table to estimate P'(T) for T = 303, 313, 323, 333, 343 by computing the SDQ given by Eq. (1) with h = 10. т (К) 293 303 313 323 333 343 353 P (atm) 0.0278 0.0482 0.0808 0.1311 0.2067 0.3173 0.4754
Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:In Exercises 67–73, estimate derivatives using the symmetric difference quotient (SDQ), defined as the
average of the difference quotients at h and -h:
1(f(a + h) – f(a)
f (a – h) – f(a)
-h
f (a + h) – f(a – h)
| 1
2h
The SDQ usually gives a better approximation to the derivative than the difference quotient.
67. The vapor pressure of water at temperature T (in kelvins) is the atmospheric pressure P at which no
net evaporation takes place. Use the following table to estimate P'(T) for T = 303, 313, 323, 333, 343 by
computing the SDQ given by Eq. (1) with h = 10.
т (К)
293
303
313
323
333
343
353
P (atm) 0.0278 0.0482 0.0808 0.1311 0.2067 0.3173 0.4754
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