Exploring ( sin k x ) / x Graph y = ( sin x ) / x , y = ( sin 2 x ) / x , and y = ( sin 4 x ) / x together over the interval − 2 ≤ x ≤ 2 . Where does each graph appear to cross the y -axis? Do the graphs really intersect the axis? What would you expect the graphs of y = ( sin 5 x ) / x and y = ( sin ( − 3 x ) ) / x to do as x → 0 ? Why? What about the graph of y = ( sin k x ) / x for other values of k ? Give reasons for your answers.
Exploring ( sin k x ) / x Graph y = ( sin x ) / x , y = ( sin 2 x ) / x , and y = ( sin 4 x ) / x together over the interval − 2 ≤ x ≤ 2 . Where does each graph appear to cross the y -axis? Do the graphs really intersect the axis? What would you expect the graphs of y = ( sin 5 x ) / x and y = ( sin ( − 3 x ) ) / x to do as x → 0 ? Why? What about the graph of y = ( sin k x ) / x for other values of k ? Give reasons for your answers.
Solution Summary: The author explains how the graph of functions y=(mathrmsinx)/x,
Exploring
(
sin
k
x
)
/
x
Graph
y
=
(
sin
x
)
/
x
,
y
=
(
sin
2
x
)
/
x
, and
y
=
(
sin
4
x
)
/
x
together over the interval
−
2
≤
x
≤
2
. Where does each graph appear to cross the y-axis? Do the graphs really intersect the axis? What would you expect the graphs of
y
=
(
sin
5
x
)
/
x
and
y
=
(
sin
(
−
3
x
)
)
/
x
to do as
x
→
0
? Why? What about the graph of
y
=
(
sin
k
x
)
/
x
for other values of
k
? Give reasons for your answers.
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