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A First Course In Differential Equations With Modelling Applications

Dennis G. Zill

$Math Studyset Vaia Explanations$ Math

11th Edition · 400 pages

ISBN: 9781305965720

Chapter 7: Q7-6RP (page 327)

$I F P {f (t)} = F (s) a n d F {g (t)} = G (s), t h e n L^{- 1} {F (s) G (s)} - f (t) g (t) .$

Short Answer

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The given statement is false

Step by step solution

To find the statement

It is not necessary that $L^{- 1} {F (s) G (s)} - f (t) g (t)$

The given statement is false

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Most popular questions from this chapter

$L^{- 1} \{\frac{e^{- 2 s}}{s^{3}}\}$

In Problems $37 - 48$ find either $F (s)$ or $f (t)$ , as indicated. $L^{- 1} \{\frac{e^{- 2 s}}{s^{2} (s - 1)}\}$

In Problems 40–54, match the given graph with one of the functions in (a)-(f). The graph is given as Figure 7.3.11.

$a) f (t) - f (t) u (t - a) b) f (t - b) u (t - b) c) f (t) u (t - a) d) f (t) - f (t) u (t - b) e) f (t) u (t - a) - f (t) u (t - b) f) f (t - a) u (t - a) - f (t - a) u (t - b)$

Figure graph for problem 52

If $L {f (t)} = F (s)$ and $a > 0$ is a constant, show that

$L {f (at)} = \frac{1}{a} F (\frac{s}{a})$

This result is known as the change of scale theorem.

(a) Use the Laplace transform to find the currentin a single-loop series circuit when $(0) = 0, L = 1 h, R = 10 Ω$ and is given in Figure $7.3.22$ .

(b) Use a graphing utility to graph $i (t) for 0 ⩽ t ⩽ 6$ . Use the graph to estimate $i_{m a x}$ and $i_{m i n}$ , the maximum and minimum values for the current.

Figure $7.3.22$ in Problem 75.

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$I F P {f (t)} = F (s) a n d F {g (t)} = G (s), t h e n L^{- 1} {F (s) G (s)} - f (t) g (t) .$

Short Answer

Step by step solution

To find the statement

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IFP{f(t)}=F(s)andF{g(t)}=G(s),thenL-1{F(s)G(s)}-f(t)g(t).

Short Answer

Step by step solution

To find the statement

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$I F P {f (t)} = F (s) a n d F {g (t)} = G (s), t h e n L^{- 1} {F (s) G (s)} - f (t) g (t) .$