テイラー log_{3}(x)

Topic

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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

simplify solve for inverse tangent line

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taylor log₃(x)

Solution

1ln(3) (x−1)−12ln(3) (x−1)²+13ln(3) (x−1)³−14ln(3) (x−1)⁴+15ln(3) (x−1)⁵+…

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Solution steps

One step at a time

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+ddx (log₃(x))(1)1! (x−1)+d²dx² (log₃(x))(1)2! (x−1)²+d³dx³ (log₃(x))(1)3! (x−1)³+…

Evaluate Derivatives

=0+1ln(3) 1! (x−1)+−1ln(3) 2! (x−1)²+2ln(3) 3! (x−1)³+−6ln(3) 4! (x−1)⁴+24ln(3) 5! (x−1)⁵+…

Refine

=1ln(3) (x−1)−12ln(3) (x−1)²+13ln(3) (x−1)³−14ln(3) (x−1)⁴+15ln(3) (x−1)⁵+…

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Notebook

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

テイラー log_{3}(x)

Solution

Solution steps

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