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expand (3x-10)^2-(7y-1)^2

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

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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 πcot(x)

Solution

πcot(1)−πcsc²(1)(x−1)+πcsc²(1)cot(1)(x−1)²+π(−csc⁴(1)−2csc²(1)cot²(1))3 (x−1)³+π(4cot³(1)csc²(1)+8csc⁴(1)cot(1))12 (x−1)⁴+…

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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

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

Evaluate Derivatives

=πcot(1)+−πcsc²(1)1! (x−1)+2πcsc²(1)cot(1)2! (x−1)²+2π(−2csc²(1)cot²(1)−csc⁴(1))3! (x−1)³+2π(4cot³(1)csc²(1)+8csc⁴(1)cot(1))4! (x−1)⁴+…

بسّط

=πcot(1)−πcsc²(1)(x−1)+πcsc²(1)cot(1)(x−1)²+π(−csc⁴(1)−2csc²(1)cot²(1))3 (x−1)³+π(4cot³(1)csc²(1)+8csc⁴(1)cot(1))12 (x−1)⁴+…

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

expand (3x-10)^2-(7y-1)^2

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