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My instructor doesn't have the most intelligible answer keys. Could you explain how to solve this?...

My instructor doesn't have the most intelligible answer keys. Could you explain how to solve this?

Math 266, Quiz 15: Answers due today, April 22, by 1:00 PM via email.

1. Let g(t) be given by

?(?) = {

0, 0 < ? < 1

? − 1, 1 < ? < 2

3 − ?, 2 < ? < 3

1, ? > 3

Rewriting ?(?) using the unit step function gives:

a) ?(?) = (? − 1)?(? − 1) + (4 − 2?)?(? − 2) + (? − 2)?(? − 3)

b) ?(?) = (? − 1)?(? − 1) − (? − 1)?(? − 2) + (? − 3)?(? − 2) − (? − 3)?(? − 3) + ?(? − 3)

c) ?(?) = (? − 1) − (? − 1)?(? − 2) + (3 − ?)?(? − 2) − (3 − ?)?(? − 3) + ?(? − 3)

d) ?(?) = (? − 1)?(? − 1) + (1 − ?)?(? − 2) − (? − 3)?(? − 2) + (? − 3)?(? − 3)

e) None of the above.

2. Use Laplace transforms to solve ?′′ + ? = ?(? − 1) − ?(? − 2) with ?(0) = 0, ? ′ (0) = 1

Solutions

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