limit as x approaches 0 of (sin(5x))/(2x)

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

☐²

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ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
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eigenvalues (

1	2	1
6	−1	0
−1	−2	−1

)

Solution

λ=0, λ=3, λ=−4

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(

1	2	1
6	−1	0
−1	−2	−1

)

Matrix eigenvalues

Let A be a square matrix, η a vector and λ a scalar that satisfy Aη=λη,
then λ is called the eigenvalue associated with the eigenvector η of A

The eigenvalues of A are the roots of the characteristic equation det(A−λ I)=0

det((

1	2	1
6	−1	0
−1	−2	−1

)−λ(

1	0	0
0	1	0
0	0	1

)): −λ³−λ²+12λ

Solve −λ³−λ²+12λ=0: λ=0, λ=3, λ=−4

The eigenvalues are:

λ=0, λ=3, λ=−4

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

limit as x approaches 0 of (sin(5x))/(2x)

Solution

Solution steps

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