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amplitude of 3cos(2x+pi/4)+1

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

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factor (6x−4)²−(5y−10)²

Solution

(6x−14+5y)(6x−5y+6)

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Solution steps

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lim_{x→ ∞}(10x−1914x−10 )

Divide by highest denominator power: 10−19x 14−10x

=lim_{x→ ∞}(10−19x 14−10x )

lim_x→a[f(x)g(x) ]=lim_x→af(x)lim_x→ag(x) , lim_x→ag(x)≠0
With the exception of indeterminate form

=lim_{x→ ∞}(10−19x )lim_{x→ ∞}(14−10x )

lim_{x→ ∞}(10−19x )=10

lim_{x→ ∞}(14−10x )=14

=1014

Cancel the common factor: 2

=57

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

amplitude of 3cos(2x+pi/4)+1

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