A function H: [a, b] → R that measures the temperature on a particularday in Hoboken is sampled at N evenly-spaced times=a = t₁

We have to find the derivative H’(t) at time t=tn where 1<n<N.

Answered: A function H: [a, b] → R that measures…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A stone is tossed into the air from ground level with an initial velocity of 35 m/s. Its height at time t is h(t) = 35t – 4.9t2 m. Compute the stone's average velocity ī in m/s over the time intervals [1, 1.01], [1, 1.001], [1, 1.0001] and [0.9999, 1], [0.999, 1], [0.99, 1]. (Use decimal notation. Give your answers to three decimal places.) Ü1,1.01] = m/s Ü[1,1.001] = m/s Ū[1,1.0001] = m/s Üj0.9999.1] = m/s U[0.999,1] = m/s Uj0.99,1] = m/s Estimate the instantaneous velocity at t = 1. (Use decimal notation. Give your answer to one decimal place.) U = m/s
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1) The data below gives P = f(t), the number of households, in millions, in the US with cable television t years since %3D 1998. 0. 4 6. 8. 10 64.65 66.25 66.73 65.73 65.14 64.87 a) Does f'(4) appear to be positive or negative or zero? Write a sentence interpreting the importance of this result. b) Estimate f'(2) and f'(10) each time writing a sentence interpreting the value.
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Calculate the average rate of change of the given function f over the intervals [a, a + h] where h = 1, 0.1, 0.01, 0.001, and 0.0001. (Technology is recommended for the cases h = 0.01, 0.001, and 0.0001.) (Round your answers to seven decimal places.) f(x) = X; a = 1 h = 1 h = 0.1 h = 0.01 h = 0.001 h = 0.0001 Need Help? Read It Watch It

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A function H: [a, b] → R that measures the temperature on a particular day in Hoboken is sampled at N evenly-spaced times a = t₁