2 tens 1 one x 10 unit form
1 answer:
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Answer:
L(f(t)) =
Step-by-step explanation:
let f be a function defined for t ≥ 0
we can write the function f(t) in terms of unit function as follows
f(t) = 2 u,(t) - 1 where
0≤ t < 1
f(t) = (2 * 0) -1 = -1
when t ≥ 1
f(t) = (2*1 )- 1 = 1
Now the Laplace transform L(F(T)) = 2L( u, (t) ) - L(1) --------equation 1
this is because L(u,(t)) =
c = 1 hence L(1) = 1/s
back to equation 1
L(f(t)) = 2 - 1/s laplace transform
also L(u(t) ) =
Well, what's the graph of say y = 5x - 2?
the line will come by graphing that, y = 5x - 2... then we check the points that lie on either side of the line.
for example... the point (0,4) is a point that lies on the left-hand-side of that line..... so... let's check for its true/false value
(0, 4) x = 0, y = 4
y < 5x - 2
4 < 5(0) - 2
4 < 0 - 2
4 < -2 <--- now, is that true? is 4 lesser than -2? well, nope
so, that means the region where 0,4 lies, is the FALSE region, and we do not shade that part, so the part that needs shading is the other side.
The boundary line is dashed, meaning, it DOES NOT include the points lying on that line, but just anything off that, because y < 5x - 2, means "y" is less than, NOT EQUALS OR LESS, but just less.
check the picture below.
the line will come by graphing that, y = 5x - 2... then we check the points that lie on either side of the line.
for example... the point (0,4) is a point that lies on the left-hand-side of that line..... so... let's check for its true/false value
(0, 4) x = 0, y = 4
y < 5x - 2
4 < 5(0) - 2
4 < 0 - 2
4 < -2 <--- now, is that true? is 4 lesser than -2? well, nope
so, that means the region where 0,4 lies, is the FALSE region, and we do not shade that part, so the part that needs shading is the other side.
The boundary line is dashed, meaning, it DOES NOT include the points lying on that line, but just anything off that, because y < 5x - 2, means "y" is less than, NOT EQUALS OR LESS, but just less.
check the picture below.