laplace transform cos^3(t)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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range −(x+3)²20 +1

Solution

f(x)≤ 1

Interval Notation

(−∞ , 1]

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Solution steps

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L{cos³(t)}

Rewrite using trig identities

L{14 cos(3t)+34 cos(t)}

Use the linearity property of Laplace Transform:
For functions f(t), g(t) and constants a, b: L{a·f(t)+b·g(t)}=a·L{f(t)}+b·L{g(t)}

=14 L{cos(3t)}+34 L{cos(t)}

L{cos(3t)}: ss²+9

L{cos(t)}: ss²+1

=14 · ss²+9 +34 · ss²+1

Refine 14 · ss²+9 +34 · ss²+1 : s4(s²+9) +3s4(s²+1)

=s4(s²+9) +3s4(s²+1)

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domain −(x+3)²20 +1

vertices −(x+3)²20 +1

inverse −(x+3)²20 +1

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

laplace transform cos^3(t)

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