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long division with remainder 121/19

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

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≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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laplace transformation g(t)=3sinh(2t)+3sin(2t)

Solution

6s²−4 +6s²+4

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Solution steps

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L{3sinh(2t)+3sin(2t)}

Verwende die lineare Eigenschaft der Laplace-Transformation:
Für Funktionen f(t), g(t) und Konstanten a, b: L{a·f(t)+b·g(t)}=a·L{f(t)}+b·L{g(t)}

=3L{sinh(2t)}+3L{sin(2t)}

L{sinh(2t)}: 2s²−4

L{sin(2t)}: 2s²+4

=3· 2s²−4 +3· 2s²+4

Fasse 3· 2s²−4 +3· 2s²+4 zusammen: 6s²−4 +6s²+4

=6s²−4 +6s²+4

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inverse laplace transformation g(t)=3sinh(2t)+3sin(2t)

Long Division with Remainder Examples

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

long division with remainder 121/19

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