To determine To sketch: The graph of the given function on the interval t ≥ 0 . Explanation The function is given as g ( t ) = u 1 ( t ) + 2 u 3 ( t ) − 6 u 4 ( t ) . The unit step function is defined as u c ( t ) = { 0 , t < c 1 , t ≥ c . As there are three different values of c in the function and t ≥ 0 , the number of intervals involved in the function is four. That is, the intervals are 0 ≤ t < 1 , 1 ≤ t < 3 , 3 ≤ t < 4 and 4 ≤ t < ∞ . For the interval 0 ≤ t < 1 , the value of the function becomes g ( t ) = 0 + 2 ( 0 ) − 6 ( 0 ) = 0 . For the interval 1 ≤ t < 3 , the value of the function becomes g ( t ) = ( 1 ) + 2 ( 0 ) − 6 ( 0 ) = 1

10th Edition

ISBN: 9780470458327

Author: William E. Boyce, Richard C. DiPrima

Publisher: Wiley, John & Sons, Incorporated

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Chapter 6.3, Problem 1P

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To sketch: The graph of the given function on the interval t≥0.

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Chapter 6.2, Problem 39P

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Elementary Differential Equations

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