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taylor sin(2t)

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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taylor sin(2t)

Solution

2t−43 t³+415 t⁵−8315 t⁷+42835 t⁹+…

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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

=0+ddt (sin(2t))(0)1! t+d²dt² (sin(2t))(0)2! t²+d³dt³ (sin(2t))(0)3! t³+…

Evaluate Derivatives

=0+21! t+02! t²+−83! t³+04! t⁴+325! t⁵+06! t⁶+−1287! t⁷+08! t⁸+5129! t⁹+…

Refine

=2t−43 t³+415 t⁵−8315 t⁷+42835 t⁹+…

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

taylor sin(2t)

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