Show that f ( x ) has a jump discontinuity at x = 10 by calculating the limits from the left and right at x = 10 .

Question

Let f(x)={3x−3ifx<104x+4   ifx≥10Show that f(x) has a jump discontinuity at x=10 by calculating the limits from the left and right at x=10.

limx→10−  f(x)=

limx→10+  f(x)= 

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Answer 1

Recall that the function is only continuous if lim_{x-> a} f(x) = f(a). For the overall limit to exist the left and right limits have to be the same. Here they are not. Thus, it can't be continuous.

lim_x->10 - is the limit from the LEFT side (going toward x=10 from x=-inf side) . Because this branch of the piece-wise function is a polynomial, we can simply plug in the value. Thus, lim_x->10 - f(x) = 3(10) - 3 = 27 .

For the other one sided limit, you will apply the same principles, but now from the RIGHT side.

Best of luck.