1. If L{f(t)} = F(s), thenC)A) L{eat f(t)} = F(s + a)B) Leat f(t)} = F(sa)D)2. What is the Laplace transform of the given function1/1SF(s) = +2s2 + 16,1/11 (²= -5² + 4)2 s3. Given f(t) = e4t, what is L{t²f(t)}?1(s - 4)²1A)B) F(s) =A)B)-==A)B) F(s) =F(s) =2S32S3+C)D)s + 16s² + 162s(s 16)s² + 16C)D)L{eat f(t)} = F(s)eatL{eat f(t)} = F(s = a) e atf(t) = cos² (2t)?1/1(s - 4)²(s - 4)³4. What is the Laplace transform of the given function f(t) = 2t²cos² (2t)?2s³ - 96(s² + 16)³2s³ - 96(s² + 16)³F(s)=F(s)=; +2(S-4)³2C)D) F(s)F(s)Ss² + 4,41/12\s s²+16/==+2S32S3+

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Answered: 1. If L{f(t)} = F(s), then

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1. If L{f(t)} = F(s), then

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 77E

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Question

1. If L{f(t)} = F(s), then
C)
A) L{eat f(t)} = F(s + a)
B) Leat f(t)} = F(sa)
D)
2. What is the Laplace transform of the given function
1/1
S
F(s) = +
2
s2 + 16,
1/1
1 (²= -5² + 4)
2 s
3. Given f(t) = e4t, what is L{t²f(t)}?
1
(s - 4)²
1
A)
B) F(s) =
A)
B)
-
==
A)
B) F(s) =
F(s) =
2
S3
2
S3
+
C)
D)
s + 16
s² + 16
2s(s 16)
s² + 16
C)
D)
L{eat f(t)} = F(s)eat
L{eat f(t)} = F(s = a) e at
f(t) = cos² (2t)?
1/1
(s - 4)²
(s - 4)³
4. What is the Laplace transform of the given function f(t) = 2t²cos² (2t)?
2s³ - 96
(s² + 16)³
2s³ - 96
(s² + 16)³
F(s)
=
F(s)=; +
2
(S-4)³
2
C)
D) F(s)
F(s)
S
s² + 4,
4
1/1
2\s s²+16/
=
=
+
2
S3
2
S3
+

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