GATE Civil Engineering (CE) 2018 Shift 2 Solved Paper

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Question : 62 of 65

Marks: +1, -0

The Laplace transform

F(s)

of the exponential function,

f(t)=e^{a t}

when

t ≥ 0

, where

a

is a constant and

(s-a)>0

, is

$\;{1}/{s+a}$
$\;{1}/{s-a}$
$\;{1}/{a-5}$
$∞$

Solution:

L(e^{x t}) \;\; =\;{1}/{S-a}

L(a^{x t}) \;\; =∫↙{0}↖{∞} e^{-s t} d t=∫↙{0}↖{∞} e^{-(s-a) t} d t

={e^{-(s-a) t}}/{-(s-a)}|_{0} ^{∞}={1}/{s-a}(0-1)={1}/{s-a}

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