Problems 143 − 152 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Use the Intermediate Value Theorem to show that the function f ( x ) = 4 x 3 − 2 x 2 − 7 has a real zero in the interval [ 1 , 2 ] .
Problems 143 − 152 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Use the Intermediate Value Theorem to show that the function f ( x ) = 4 x 3 − 2 x 2 − 7 has a real zero in the interval [ 1 , 2 ] .
Solution Summary: The author explains the intermediate value theorem that for f is a polynomial function and the interval is [1,2].
Problems
143
−
152
are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.
Use the Intermediate Value Theorem to show that the function
f
(
x
)
=
4
x
3
−
2
x
2
−
7
has a real zero in the interval
[
1
,
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 4 Solutions
Pearson eText for Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry -- Instant Access (Pearson+)
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