Chapter 1: Limits
Section 1.6: Continuity
Show that the function fx=sinx/x is discontinuous at x=0.
The graph of f in Figure 1.6.3(a) suggests that this function is discontinuous at x=0 because it has a jump there, that is, the limits from the left and right will be different.
Indeed, limx→0−sinxx = −1 and limx→0+sinxx = 1
Hence, limx→0fx does not exist, so f cannot be continuous at x=0.
Figure 1.6.3(a) Graph of sinx/x
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