(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.
The height above the ground of a rider on a Ferris wheel can be modeled by the sinusoidal function
h=6sin(1.05t−1.57)+8ℎ=6sin(1.05t-1.57)+8
where hℎ is the height of the rider above the ground, in metres, and t is the time, in minutes, after the ride starts.
When the rider is at least 11.5 m above the ground, she can see the rodeo grounds. During each rotation of the Ferris wheel, the length of time that the rider can see the rodeo grounds, to the nearest tenth of a minute, is min.
How do the slopes of the lines tangent to the graph of y = tan-1 x behave as x S ∞?
Q) Plot, on the same figure, two
related functions of y1 = sin? (x) and
y2 = cos (2x), in the interval O
University Calculus: Early Transcendentals (3rd Edition)
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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