We have the following three conclusions about the piecewise function evaluated at x = 14.75:
- [tex]\lim_{t \to 14.75^{-}} f(t) = 66[/tex].
- [tex]\lim_{t \to 14.75^{+}} f(t) = 10[/tex].
- [tex]\lim_{t \to 14.75} f(t)[/tex] does not exist as [tex]\lim_{t \to 14.75^{-}} f(t) \ne \lim_{t \to 14.75^{+}} f(t)[/tex].
How to determinate the limit in a piecewise function
In a piecewise function, the limit for a given value exists when the two lateral limits are the same and, thus, continuity is guaranteed. Otherwise, the limit does not exist.
According to the definition of lateral limit and by observing carefully the figure, we have the following conclusions:
- [tex]\lim_{t \to 14.75^{-}} f(t) = 66[/tex].
- [tex]\lim_{t \to 14.75^{+}} f(t) = 10[/tex].
- [tex]\lim_{t \to 14.75} f(t)[/tex] does not exist as [tex]\lim_{t \to 14.75^{-}} f(t) \ne \lim_{t \to 14.75^{+}} f(t)[/tex].
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