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taylor cos(3x+2)

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

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log_□

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ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
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taylor cos(3x+2)

Solution

cos(2)−3sin(2)x−9cos(2)2 x²+9sin(2)2 x³+27cos(2)8 x⁴+…

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Taylor Series

Taylor series of function f(x) at a is defined as:
f(x)=f(a)+f^′(a)1! (x−a)+f^′′(a)2! (x−a)²+f^′′′(a)3! (x−a)³+…

Apply the Taylor Formula

=cos(2)+ddx (cos(3x+2))(0)1! x+d²dx² (cos(3x+2))(0)2! x²+d³dx³ (cos(3x+2))(0)3! x³+…

Evaluate Derivatives

=cos(2)+−3sin(2)1! x+−9cos(2)2! x²+27sin(2)3! x³+81cos(2)4! x⁴+…

Refine

=cos(2)−3sin(2)x−9cos(2)2 x²+9sin(2)2 x³+27cos(2)8 x⁴+…

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

taylor cos(3x+2)

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