Which of the following most likely explains why a graphing-calculator plot of on the…
MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
Which of the following most likely explains why a graphing-calculator plot of y=sin(x1) on the window −10≤x≤10 and −1≤y≤1 appears to settle into a single horizontal line near x=0?
(a) Because sin(x1) approaches 0 as x→0, the graph levels off along the x–axis.
(b) The symmetric window causes the calculator to plot the positive and negative parts on top of each other, giving the illusion of a single horizontal line.
(c) The calculator evaluates only finitely many evenly–spaced x–values; near x=0 the oscillations are too rapid, so successive sampled points all lie very close to y=0, and the display connects them as a straight horizontal segment.
(d) The y–range −1≤y≤1 is so small compared with the screen’s pixel height that all the peaks and troughs fall in the same pixel row, hiding the oscillations.