(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.
Find the equation(s) of the tangent line(s) to the graph of the curve
y = x3 − 12x
through the point
(1, −12)
not on the graph. (Enter your answers as a comma-separated list of equations.)
Find the equation(s) of the tangent line(s) to the graph of the curve
y = x3 − 12x
through the point
(1, −12)
not on the graph. (Enter your answers as a comma-separated list of equations.)
How do the slopes of the lines tangent to the graph of y = tan-1 x behave as x S ∞?
1. a) Find dy for the equation 4x²y² - x³y=3
dx
b) find the x-coordinate of each point on the curve where
the tangent line is vertical
() Find the y-coordinate of each point on the curve.
with an x-coordinate of -1.
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