ii. Prove the second translation theorem (in time): If F(s) = L(f(t)), then L(ua(t)f(t – a)) = e-a® F(s) (a > 0).
ii. Prove the second translation theorem (in time): If F(s) = L(f(t)), then L(ua(t)f(t – a)) = e-a® F(s) (a > 0).
Chapter5: Exponential And Logarithmic Functions
Section5.1: Exponential Functions And Their Graphs
Problem 7ECP: Sketch the graph of fx=5e0.17x.
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A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
Part ii)
![5. Let e be a positive number and consider the function f.(x) defined by
if 0 <x< €
f.(x)=-
%3D
if x > €.
The graph of this function is shown in Figure 65. It is clear that for
every e > 0 we have Jo f.(x)dx = 1. Show that
1-e-pe
L[f.(x)] =-
pe
and
lim L[f.(x)]=1.
Strictly speaking, lim0 f.(x) does not exist as a function, so
L[lim.0 f.(x)]is not defined; but if we throw caution to the winds, then
8(x) = lim f.(x)
1/ɛ
FIGURE 65](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe25f92a2-1c4d-41a3-af19-0cdf00d27604%2Fd724cf5e-af93-44ae-9e54-721a3fadd1cf%2Fv93m9l8_processed.png&w=3840&q=75)
Transcribed Image Text:5. Let e be a positive number and consider the function f.(x) defined by
if 0 <x< €
f.(x)=-
%3D
if x > €.
The graph of this function is shown in Figure 65. It is clear that for
every e > 0 we have Jo f.(x)dx = 1. Show that
1-e-pe
L[f.(x)] =-
pe
and
lim L[f.(x)]=1.
Strictly speaking, lim0 f.(x) does not exist as a function, so
L[lim.0 f.(x)]is not defined; but if we throw caution to the winds, then
8(x) = lim f.(x)
1/ɛ
FIGURE 65
Transcribed Image Text:ii. Prove the second translation theorem (in time): If F(s) = L(f (t)), then
L(ua(t)f(t – a)) = e_a$ F(s) (a > 0).
-as
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