find the asymptotes of the curve : y = 2x^2 - 1 + 3x^3 / 3 - 2x^2
Answers
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0
Answer:
Vertical Asymptotes:
x
=
0
∧
x
=
−
3
2
Horizontal Asymptote:
y
=
−
1
Explanation:
y
=
2
x
2
+
1
3
x
−
2
x
2
=
−
2
x
2
+
1
2
x
2
+
3
x
=
−
2
x
2
+
1
x
(
2
x
+
3
)
Verical Asymptotes
Since denominator could not be 0
we find the possible values of x that would make the equation in the denominator 0
x
(
2
x
+
3
)
=
0
Therefore
x
=
0
(
2
x
+
3
)
=
0
⇒
x
=
−
3
2
are vertical asymptotes.
Horizontal asymptotes
Since the degree of numerator and denominator is the same, we have an horizontal asymptotes
y
≈
−
2
x
2
2
x
2
=
−
1
∴
y
=
−
1
is a horizontal asymptotes for
x
→
±
∞
graph{-(2x^2+1)/(x(2x+3)) [-25.66, 25.65, -12.83, 12.82]}
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