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A functionf(x)is said to have a jump discontinuity atx=a if all three of the following conditions hold: limxaf(x)exists. limxa+f(x)exists. The left and right limits are
A functionf(x)is said to have ajumpdiscontinuity atx=a if all three of the following conditions hold:
- limxaf(x)exists.
- limxa+f(x)exists.
- The left and right limits are not equal.
Show that
f(x)={7x-3} ifx<4
{5/x+4} ifx4
has a jump discontinuity atx=4 by calculating the limit asx approaches 4 from the left and from the right.
limx4f(x)=
limx4+f(x)=
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