(a) Sketch the curves y = ± e − x / 2 and y = e − x / 2 sin 2 x for − π / 2 ≤ x ≤ 3 π / 2 in the same coordinate system , and check your work using a graphing utility. (b) Find all x -intercepts of the curve y = e − x / 2 sin 2 x in the stated interval, and find x -coordinates of all points where this curve intersects the curves y = ± e − x / 2 .
(a) Sketch the curves y = ± e − x / 2 and y = e − x / 2 sin 2 x for − π / 2 ≤ x ≤ 3 π / 2 in the same coordinate system , and check your work using a graphing utility. (b) Find all x -intercepts of the curve y = e − x / 2 sin 2 x in the stated interval, and find x -coordinates of all points where this curve intersects the curves y = ± e − x / 2 .
(a) Sketch the curves
y
=
±
e
−
x
/
2
and
y
=
e
−
x
/
2
sin
2
x
for
−
π
/
2
≤
x
≤
3
π
/
2
in the same coordinate system, and check your work using a graphing utility.
(b) Find all x-intercepts of the curve
y
=
e
−
x
/
2
sin
2
x
in the stated interval, and find x-coordinates of all points where this curve intersects the curves
y
=
±
e
−
x
/
2
.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
Q1 Find all the points of intersections of the curves r = 1+cose and r=1+sin0
r-1+ (0)
r=1+cm(0)
Q) Plot, on the same figure, two
related functions of y1 = sin? (x) and
y2 = cos (2x), in the interval O
A fun ride for children follows the curve with equation
y = /2 sin
+ V2 cos
12
+2, 0sxs 24, where y is the height from the
12
ground in metres and x is the horizontal distance travelled.
Express Z sin x) + Jz cos
-x | in the form r cos
12
b
What is the maximum height of the fun ride?
Sketch the graph of the curve y =
2 sin
12
x |+2,
12
+
cos
0
Chapter 1 Solutions
Calculus Early Transcendentals, Binder Ready Version
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY