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prove (sin^3(x)+cos^3(x))/(sin(x)+cos(x))=1-sin(x)cos(x)

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(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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matriz escalonada (

1	2
0	−1

)

Solution

(

1	2
0	−1

)

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(

5	2	3
5	−1	−7
13	6	27

)

Vetores próprios de uma matriz

Seja A uma matriz quadrada, η um vetor e λ um escalar que satisfaça Aη=λη,
então η é um vetor próprio de A e λ é o valor próprio associado a ele

Para encontrar os vetores próprios η, resolver (A−λ I)η=0 para cada valor próprio λ

Encontrar os valores próprios de (

5	2	3
5	−1	−7
13	6	27

): λ≈ −1.65343…, λ≈ 5.52989…, λ≈ 27.12353…

Vetores próprios de λ=−1.65343…: (

2.82364…

−10.89346…

)

Vetores próprios de λ=5.52989…: (

−0.85471…

−1.72645…

)

Vetores próprios de λ=27.12353…: (

0.11494…

−0.22846…

)

Os vetores próprios de (

5	2	3
5	−1	−7
13	6	27

)

2.82364…

−10.89346…

), (

−0.85471…

−1.72645…

), (

0.11494…

−0.22846…

)

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

prove (sin^3(x)+cos^3(x))/(sin(x)+cos(x))=1-sin(x)cos(x)

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