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derivative of (4x+3+(-8x-1))

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

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lim_{x→ 0}(1−cos(x)x² )

Solution

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0.5

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lim_{x→ 0}(1−cos(x)x² )

Apply L'Hopital's Rule: lim_{x→ 0}(sin(x)2x )

=lim_{x→ 0}(sin(x)2x )

Apply L'Hopital's Rule: lim_{x→ 0}(cos(x)2 )

=lim_{x→ 0}(cos(x)2 )

Plug in the value x=0

=cos(0)2

Use the following trivial identity: cos(0)=1

cos(x) periodicity table with 2πn cycle:

`x`	cos(`x`)	`x`	cos(`x`)
0	1	π	−1
π6	√32	7π6	−√32
π4	√22	5π4	−√22
π3	12	4π3	−12
π2	0	3π2	0
2π3	−12	5π3	12
3π4	−√22	7π4	√22
5π6	−√32	11π6	√32

=12

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

derivative of (4x+3+(-8x-1))

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