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points of d'intersection 4x+5

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

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ddx

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

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transformation de laplace 2cos³(x)

Solution

s2(s²+9) +3s2(s²+1)

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Solution steps

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L{2cos³(x)}

Récrire en utilisant des identités trigonométriques

L{12 cos(3x)+32 cos(x)}

Utiliser la propriété de linéarité de la transformée de Laplace :
Pour les fonctions f(t), g(t) et les constantes a, b: L{a·f(t)+b·g(t)}=a·L{f(t)}+b·L{g(t)}

=12 L{cos(3x)}+32 L{cos(x)}

L{cos(3x)}: ss²+9

L{cos(x)}: ss²+1

=12 · ss²+9 +32 · ss²+1

Redéfinir 12 · ss²+9 +32 · ss²+1 : s2(s²+9) +3s2(s²+1)

=s2(s²+9) +3s2(s²+1)

Solve instead

inverser laplace 2cos³(x)

Order of operations two-step without parentheses Examples

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

points of d'intersection 4x+5

Solution

Solution steps

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