Is the function f(x) of exponential order?

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...
icon
Related questions
Question

Explain this examples

Is the function f(x) of exponential order?
X
What is meant by exponential order?
A function f(x) is of exponential order if there exist an
exponential function that is greater that | f(t)| as t →o.
If a function is piecewise continuous and of exponential
order then the Laplace transform of the function exists.
f(t) is of exponential order if there exist finite constant
M, a and T such that f(t) < Me“ for t>t,
Examples
The following functions are of exponential order
f(t) = sin(10t)
М —
M = 2, t, = 0, a = 0
f (t) = 20t +1
M = 20, t, = 1,a = 1
f (t) = 2'
f (t) = e'01
The following functions are NOT of exponential order
M =1, t, = 0,a =1
M- 1.1, t, 0,α -10
10t
f (t) = e?r*+1
f (t) = 2*+0.
3+0.5
Transcribed Image Text:Is the function f(x) of exponential order? X What is meant by exponential order? A function f(x) is of exponential order if there exist an exponential function that is greater that | f(t)| as t →o. If a function is piecewise continuous and of exponential order then the Laplace transform of the function exists. f(t) is of exponential order if there exist finite constant M, a and T such that f(t) < Me“ for t>t, Examples The following functions are of exponential order f(t) = sin(10t) М — M = 2, t, = 0, a = 0 f (t) = 20t +1 M = 20, t, = 1,a = 1 f (t) = 2' f (t) = e'01 The following functions are NOT of exponential order M =1, t, = 0,a =1 M- 1.1, t, 0,α -10 10t f (t) = e?r*+1 f (t) = 2*+0. 3+0.5
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning