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amplitude of 2sin(2x)+3

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

☐²

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√☐

^□√☐

□□

log_□

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ddx

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

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taylor cos(−2x)

Solution

1−2x²+23 x⁴−445 x⁶+2315 x⁸+…

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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

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

Evaluate Derivatives

=1+01! x+−42! x²+03! x³+164! x⁴+05! x⁵+−646! x⁶+07! x⁷+2568! x⁸+…

Refine

=1−2x²+23 x⁴−445 x⁶+2315 x⁸+…

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

amplitude of 2sin(2x)+3

Solution

Solution steps

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