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axis x^2+y^2=1

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

☐²

x^☐

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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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intercepts 30−x³

Solution

X Intercepts: (³√30, 0), Y Intercepts: (0, 30)

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Solution steps

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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 (e^−x²)(0)1! x+d²dx² (e^−x²)(0)2! x²+d³dx³ (e^−x²)(0)3! x³+…

Evaluate Derivatives

=1+01! x+−22! x²+03! x³+124! x⁴+05! x⁵+−1206! x⁶+07! x⁷+16808! x⁸+…

بسّط

=1−x²+12 x⁴−16 x⁶+124 x⁸+…

Derivative Sum/Diff Rule Examples

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

axis x^2+y^2=1

Solution

Solution steps

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