In Problems 7 − 26 , graph the plane curve whose parametric equations are given, and show its orientation. Find the rectangular equation of each curve. x ( t ) = sin 2 t , y ( t ) = cos 2 t ; 0 ≤ t ≤ 2 π
In Problems 7 − 26 , graph the plane curve whose parametric equations are given, and show its orientation. Find the rectangular equation of each curve. x ( t ) = sin 2 t , y ( t ) = cos 2 t ; 0 ≤ t ≤ 2 π
Solution Summary: The author explains how to draw the parametric equation by plugging some values of t in the given equation and finding few points on the curve.
In Problems
7
−
26
,
graph the plane curve whose parametric equations are given, and show its orientation. Find the rectangular equation of each curve.
x
(
t
)
=
sin
2
t
,
y
(
t
)
=
cos
2
t
;
0
≤
t
≤
2
π
EXAMPLE 3
Find
S
X
√√2-2x2
dx.
SOLUTION Let u = 2 - 2x². Then du =
Χ
dx =
2- 2x²
=
信
du
dx, so x dx =
du and
u-1/2 du
(2√u) + C
+ C (in terms of x).
Let g(z) =
z-i
z+i'
(a) Evaluate g(i) and g(1).
(b) Evaluate the limits
lim g(z), and lim g(z).
2-12
(c) Find the image of the real axis under g.
(d) Find the image of the upper half plane {z: Iz > 0} under the function g.
Chapter 9 Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY