In Exercises 33–40 , which of the following functions have the given property? I . y = x 2 − 2 x 2 + 2 II . y = x 2 + 2 x 2 − 2 III . y = ( x − 1 ) ( 1 − x ) ( x + 1 ) 2 IV . y = x 3 − x V . y = x − 1 x VI . y = ( x 2 − 2 ) ( x 2 + 2 ) More than two distinct zeros.
In Exercises 33–40 , which of the following functions have the given property? I . y = x 2 − 2 x 2 + 2 II . y = x 2 + 2 x 2 − 2 III . y = ( x − 1 ) ( 1 − x ) ( x + 1 ) 2 IV . y = x 3 − x V . y = x − 1 x VI . y = ( x 2 − 2 ) ( x 2 + 2 ) More than two distinct zeros.
In Exercises 33–40, which of the following functions have the given property?
I
.
y
=
x
2
−
2
x
2
+
2
II
.
y
=
x
2
+
2
x
2
−
2
III
.
y
=
(
x
−
1
)
(
1
−
x
)
(
x
+
1
)
2
IV
.
y
=
x
3
−
x
V
.
y
=
x
−
1
x
VI
.
y
=
(
x
2
−
2
)
(
x
2
+
2
)
Points z1 and z2 are shown on the graph.z1 is at (4 real,6 imaginary), z2 is at (-5 real, 2 imaginary)Part A: Identify the points in standard form and find the distance between them.Part B: Give the complex conjugate of z2 and explain how to find it geometrically.Part C: Find z2 − z1 geometrically and explain your steps.
A polar curve is represented by the equation r1 = 7 + 4cos θ.Part A: What type of limaçon is this curve? Justify your answer using the constants in the equation.Part B: Is the curve symmetrical to the polar axis or the line θ = pi/2 Justify your answer algebraically.Part C: What are the two main differences between the graphs of r1 = 7 + 4cos θ and r2 = 4 + 4cos θ?
A curve, described by x2 + y2 + 8x = 0, has a point A at (−4, 4) on the curve.Part A: What are the polar coordinates of A? Give an exact answer.Part B: What is the polar form of the equation? What type of polar curve is this?Part C: What is the directed distance when Ø = 5pi/6 Give an exact answer.
Chapter 1 Solutions
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