The Dirac delta function 8(t) may also be characterized by the following two properties. t#0, 0, 8(t) = . and s(t)dt = 1 "infinite," t= 0, Formally using the mean value theorem for definite integrals, verify that if f(t) is continuous, then the above properties imply the following. | f(t)8(t)dt = f(0) State the mean value theorem for definite integrals for a continuous function f(t). There exists a value c in the interval such that f(c) =
The Dirac delta function 8(t) may also be characterized by the following two properties. t#0, 0, 8(t) = . and s(t)dt = 1 "infinite," t= 0, Formally using the mean value theorem for definite integrals, verify that if f(t) is continuous, then the above properties imply the following. | f(t)8(t)dt = f(0) State the mean value theorem for definite integrals for a continuous function f(t). There exists a value c in the interval such that f(c) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The Dirac delta function 8(t) may also be characterized by the following two properties.
0,
8(t) =
t# 0,
| 8(t)dt = 1
and
"infinite," t= 0,
- 0o
Formally using the mean value theorem for definite integrals, verify that if f(t) is continuous, then the above properties imply the following.
| f(t)8(t)dt = f(0)
State the mean value theorem for definite integrals for a continuous function f(t).
There exists a value c in the interval
such that f(c) =
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