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focos y=3x^2-x-2

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(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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derivada implícita dydx , x⁷y¹²+13x⁵+14y¹⁵=19

Solution

dydx =−7x⁶y¹²−65x⁴6y¹¹(2x⁷+35y³)

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Parabola Directrix

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (the directrix)

Parabola standard equation

4p(y−k)=(x−h)² is the standard equation for an up-down facing parabola with vertex at (h, k),
and a focal length |p|

Rewrite y=−3x²−2x+65 in the standard form

4(−512 )(y−1915 )=(x−(−13 ))²

(h, k)=(−13 , 1915 ), p=−512

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance −p from the center (−13 , 1915 ) y-coordinate

y=1915 −p

y=1915 −(−512 )

Refine

y=10160

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

focos y=3x^2-x-2

Solution

Solution steps

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