Since we are slicing with respect to x
, we must express the side length s
in terms of x
. Thus, we describe the curves in the image as functions of x
.
Note that the parabola x=4−y2
must be described using
2
functions of x
. In fact, solving for y
, we obtain y=+
sqrt(4-x)
and y=−
sqrt(4-x)
.
Note that the parabola x=4−y2
does not pass the vertical line test, so it must be described using
2
functions of x
. This also arises as an algebraic consequence when we solve for y
since we must consider the positive and negative square roots. In fact, solving for y
gives y=+
sqrt(4-x)
and y=−
sqrt(4-x)
.>
Redundancy in the textbook:
Note that the parabola x=4−y2 must be described using 2 functions of x . In fact, solving for y , we obtain y=+ sqrt(4-x) and y=− sqrt(4-x) .
Note that the parabola x=4−y2 does not pass the vertical line test, so it must be described using 2 functions of x . This also arises as an algebraic consequence when we solve for y since we must consider the positive and negative square roots. In fact, solving for y gives y=+ sqrt(4-x) and y=− sqrt(4-x) .>
See accumulatedCrossSections/digInAccumulatedCrossSections.tex