Limits of a Piecewise Function In Exercises 33 and 34, sketch the graph of f . Then identify the values of c for which lim x → c f ( x ) exists. f ( x ) = { sin x , x < 2 1 − cos x , 0 ≤ x ≤ π cos x , x < π
Limits of a Piecewise Function In Exercises 33 and 34, sketch the graph of f . Then identify the values of c for which lim x → c f ( x ) exists. f ( x ) = { sin x , x < 2 1 − cos x , 0 ≤ x ≤ π cos x , x < π
Limits of a Piecewise Function In Exercises 33 and 34, sketch the graph of f. Then identify the values of c for which
lim
x
→
c
f
(
x
)
exists.
f
(
x
)
=
{
sin
x
,
x
<
2
1
−
cos
x
,
0
≤
x
≤
π
cos
x
,
x
<
π
Definition Definition Group of one or more functions defined at different and non-overlapping domains. The rule of a piecewise function is different for different pieces or portions of the domain.
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.
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