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Hola mi amigos. Mi llamo Drew.
I don't actually speak Spanish.
Problem 81:
y
=
−
x
2
+
x
−
2
{\displaystyle y=-x^{2}+x-2}
[
(
−
(
x
+
h
)
2
)
+
(
x
+
h
)
−
2
]
−
[
−
x
2
+
x
−
2
]
h
{\displaystyle {\frac {[(-(x+h)^{2})+(x+h)-2]-[-x^{2}+x-2]}{h}}}
Distribute -1 in original formula
[
(
−
(
x
+
h
)
2
)
+
(
x
+
h
)
−
2
]
+
[
x
2
−
x
+
2
]
h
{\displaystyle {\frac {[(-(x+h)^{2})+(x+h)-2]+[x^{2}-x+2]}{h}}}
Square the new formula
[
(
−
(
x
2
+
2
x
h
+
h
2
)
)
+
x
+
h
−
2
]
+
[
x
2
−
x
+
2
]
h
{\displaystyle {\frac {[(-(x^{2}+2xh+h^{2}))+x+h-2]+[x^{2}-x+2]}{h}}}
Negate new formula
[
(
−
x
2
−
2
x
h
−
h
2
)
+
x
+
h
−
2
]
+
[
x
2
−
x
+
2
]
h
{\displaystyle {\frac {[(-x^{2}-2xh-h^{2})+x+h-2]+[x^{2}-x+2]}{h}}}
Change format
[
−
x
2
−
2
x
h
−
h
2
+
x
+
h
−
2
]
+
[
x
2
−
x
+
2
]
h
{\displaystyle {\frac {[-x^{2}-2xh-h^{2}+x+h-2]+[x^{2}-x+2]}{h}}}
Change format
Failed to parse (Conversion error. Server ("/media/api/rest_") reported: "Cannot get mml. upstream connect error or disconnect/reset before headers. reset reason: connection termination"): {\displaystyle {\frac {-x^{2}-2xh-h^{2}+x+h-2+x^{2}-x+2}{h}}}
Organize to cancel out
−
x
2
+
x
2
−
2
x
h
−
h
2
+
h
+
x
−
x
−
2
+
2
h
{\displaystyle {\frac {-x^{2}+x^{2}-2xh-h^{2}+h+x-x-2+2}{h}}}
Cancel items
−
2
x
h
−
h
2
+
h
h
{\displaystyle {\frac {-2xh-h^{2}+h}{h}}}
Difference formula:
2
x
−
h
+
1
{\displaystyle 2x-h+1}
![{\displaystyle {\frac {[(-(x+h)^{2})+(x+h)-2]-[-x^{2}+x-2]}{h}}}](/media/api/rest_v1/media/math/render/svg/14dd8124b5e79a0c52fd5ae6c90c317933677216)
![{\displaystyle {\frac {[(-(x+h)^{2})+(x+h)-2]+[x^{2}-x+2]}{h}}}](/media/api/rest_v1/media/math/render/svg/c14718724423c45917d9e6c90dc97b8ab4efafe1)
![{\displaystyle {\frac {[(-(x^{2}+2xh+h^{2}))+x+h-2]+[x^{2}-x+2]}{h}}}](/media/api/rest_v1/media/math/render/svg/fdb10a189e802e0aa88dd7f9a0f8417be8c4e1dd)
![{\displaystyle {\frac {[(-x^{2}-2xh-h^{2})+x+h-2]+[x^{2}-x+2]}{h}}}](/media/api/rest_v1/media/math/render/svg/8dd90bd709ea50ce14c8837ade0a33cbec0ad6ab)
![{\displaystyle {\frac {[-x^{2}-2xh-h^{2}+x+h-2]+[x^{2}-x+2]}{h}}}](/media/api/rest_v1/media/math/render/svg/9f68fd00c4bba019bcee62621ce85b7151e9427b)
