Find the limit

Find the limit
Find the limit

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:


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:


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