1. If L{f(t)} = F(s), then A) L{eat f(t)} = F(s + a) B) L{eat f(t)} = F(s-a) 2. What is the Laplace transform of the given function 1/1 2\s 1/1 F(s) = ²2²/²2 ( 5₁ - 5² + 4) 3. Given f(t) = e4t, what is L{t²f(t)}? 1 (s - 4)² 1 A) B) A) B) F(s) = - (s - 4)² + S s²+16/ S C) D) L{eat f(t)} = F(s)eat L{eat f(t)} = F(sa)eat f(t) = cos² (2t)? 1/1 - (+²²+4) 1/1 = + C) D) F(s) C) D) F(s) =: - 2 s²+16/ 2 (s-4)³ 2 (s-4)³
1. If L{f(t)} = F(s), then A) L{eat f(t)} = F(s + a) B) L{eat f(t)} = F(s-a) 2. What is the Laplace transform of the given function 1/1 2\s 1/1 F(s) = ²2²/²2 ( 5₁ - 5² + 4) 3. Given f(t) = e4t, what is L{t²f(t)}? 1 (s - 4)² 1 A) B) A) B) F(s) = - (s - 4)² + S s²+16/ S C) D) L{eat f(t)} = F(s)eat L{eat f(t)} = F(sa)eat f(t) = cos² (2t)? 1/1 - (+²²+4) 1/1 = + C) D) F(s) C) D) F(s) =: - 2 s²+16/ 2 (s-4)³ 2 (s-4)³
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:1. If L{f(t)} = F(s), then
A)
L{eat f(t)} = F(s + a)
B) L{eat f(t)} = F(sa)
2. What is the Laplace transform of the given function
1/1
A) F(s) == +
S
2 s s² + 16A
1/1 S
B) F(S) = (²+4)
3. Given f(t) = e4t, what is L{t²f(t)}?
1
(s - 4)²
1
A)
B)
A) F(s) =
S3
2
B) F(S)=3
A)
B) F(s) =
F(s) =
(s - 4)²
(s-4)³
4. What is the Laplace transform of the given function f(t) = 2t² cos² (2t)?
2 2s³ - 96
2
1
A) F(S) = -5
A) F(S)
+
B) F(s) =-
=
B) F(s) =
s + 16
S² + 16
2s(s - 16)
s² + 16
S
4 s² +1
3s +1
4(s² +9)
6. If the Laplace transform of x³/² is
3√√π
+
4 s² +9
C)
D)
5. What is the Laplace transform of the given function f(t) = cos³ (t)?
3 S
3s
s² + 1
3 S
3√√π
4s5/2
C)
D)
C)
D)
D)
C)
D)
L{eat f(t)}: = F(s)eat
L{eat f(t)} = F(s-a)eat
f(t) = cos² (2t)?
1/1
S
- (+²+)
2
s² + 4.
4
s² + 16A
F(s) =
1/1
F(s) = +
2
(s-4)³
2
D)
4² (s + 1)
√√π
4(s+1) 5/2
7. Find the Laplace transform of f(t) = (1 + sin 2t cos 2t).
s² +2s + 16
s(s² + 16)
s²+2s + 16
(s² + 16)
C)
F(S)=3+
F(s) =
D)
F(s) =
F(s) =
2
53
F(s) =
F(s) =
(s² + 16)³
2s³96
(s² + 16)³
+
4 s² + 1
,then the Laplace transform of t³/²e-t is:
C)
3√√π
F(s)=5 (s + 1)
4s²
F(s) =
4s
s² +9
+
1 S
4 s² +9
3√π
4(s+1) 5/2
s²+2s +4
s(s² + 16)
s² + 2s + 16
s(s² + 4)
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