Which functions of time correspond to the following Laplace transforms? What values will the time functions approach as time tends to infinity? F ( s ) = 1 s 2 − 1 I assumed it was a standard Laplace transformed and wrote sinh ⁡ ( t ), which is unbounded when lim t → ∞ sinh ⁡ ( t ) = ∞But the expected answer is f ( t ) = − 0.5 e − t + 0.5 e t , why is that?

Name: Which functions of time correspond to the following Laplace transforms? What values will the time functions approach as time tends to infinity? F ( s ) = 1 s 2 − 1 I assumed it was a standard Laplace transformed and wrote sinh ⁡ ( t ), which is unbounded when lim t → ∞ sinh ⁡ ( t ) = ∞But the expected answer is f ( t ) = − 0.5 e − t + 0.5 e t , why is that?
Uploaded: 2022-02-23T17:22:57+00:00
Description: Which functions of time correspond to the following Laplace transforms? What values will the time functions approach as time tends to infinity? F ( s ) = 1 s 2 − 1 I assumed it was a standard Laplace transformed and wrote sinh ⁡ ( t ), which is unbounded when lim t → ∞ sinh ⁡ ( t ) = ∞But the expected answer is f ( t ) = − 0.5 e − t + 0.5 e t , why is that?

Question

Which functions of time correspond to the following Laplace transforms? What values ​​will the time functions approach as time tends to infinity?  F  (  s  )  =      1                  s        2            −      1      I assumed it was a standard Laplace transformed and wrote   sinh  ⁡  (  t  ), which is unbounded when       lim          t      →      ∞        sinh  ⁡  (  t  )  =  ∞But the expected answer is   f  (  t  )  =  −  0.5      e          −      t        +  0.5      e    t  , why is that?

gerasseltd9 · Accepted Answer

Hyperbolic sine: the odd part of the exponential function, that is  sinh  ⁡  x  =                    e        x            −              e                  −          x                      2    =                    e                  2          x                    −      1              2              e        x              =            1      −              e                  −          2          x                            2              e                  −          x                      sinh  ⁡  (  t  )  =  −  0.5      e          −      t        +  0.5      e    t

Melina Barber · Accepted Answer

It&#039;s just the definition of the Hyperbolic Sine:  sinh  ⁡  (  x  )  =                              e          x                −                  e                      −            x                              2      Whence your result.As you can see      lim          t      →      +      ∞        sinh  ⁡  (  t  )  =      lim          t      →      +      ∞                                    e          t                −                  e                      −            t                              2        →  +  ∞

Which functions of time correspond to the following Laplace transforms? What values will the time functions approach as time tends to infinity? F(s)=(1)/(s^2−1)

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