step by step solution
The given function is
f(x)=\begin{cases}- \frac{x}{2}-\frac{5}{2},\quad{x\lt0}\\\\\ 2x+5 ,\quad\quad\quad{x\geq0}\end{cases}Notice that as x approaches 0 from the left, the function is:
f(x)=- \frac{x}{2}-\frac{5}{2}To Find the limit:
\lim_{x\to0^{-}}{f(x)}\implies\lim_{x\to0^{-}}\left({ \textcolor{primary}{- \frac{x}{2}-\frac{5}{2}}}\right)Direct Substitution Property of Limits
If a is in the domain of a polynomial or a rational function f, then:
\lim_{x\to{a}}{f(x)}=f(a)using the above property we get
\lim_{x\to0^{-}}\left({ \textcolor{primary}{- \frac{x}{2}-\frac{5}{2}}}\right)\implies \left({ {- \frac{\textcolor{primary}{0}}{2}-\frac{5}{2}}}\right)\implies -\frac{5}{2}The required answer is:
\lim_{x\to0^{-}}{f(x)}=-\frac{5}{2}Similar posts:
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