Explanation Given: The given statement is, “ F ( s ) = s 2 s 2 + 4 is not the Laplace transform of a function that is piecewise continuous and of exponential order”. Theorem used: The necessary and sufficient condition for the existence of the Laplace transform of a piecewise continuous and exponential order function f ( t ) is, lim s → ∞ { F ( s ) } = 0 Here F ( s ) = L { f ( t ) } . Calculation: From the above theorem, the given function can be expressed as follows lim s → ∞ { F ( s ) } = lim s → ∞

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ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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2 Q/ Let d₂ +d, di, d2: R² XR² R² defined as follow ((x+x), (2, 1) = √(x-2)² + (x_wx • d₁ ((x,y), (z, w)) = max {1x-z\, \y-w\} • 1 1 dq ((x,y), (Z, W)) = \ x=2\+\-w| 2 • show that dod₁, d₂ are equivalent? 2

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