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Sketch the graph of the function and use it to determine the values of $ a $ for which $ \displaystyle \lim_{x\to a}f(x) $ exists.

$ f(x) = \left\{

\begin{array}{ll}

1 + \sin x & \mbox{if $ x < 0 $}\\

\cos x & \mbox{if $ 0 \le x \le \pi $}\\

\sin x & \mbox{if $ x > \pi $}

\end{array} \right.$

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Ali L.

October 12, 2020

Okay here we have a photograph of the piecewise defined function F of X one plus one plus sine of X. When X is less than zero. F of X is defined to be co sign of X for X between zero and pi inclusive, and F of X equals sine of X. When X is greater than high. Looking at the graph of F of X, we can see that it is continuous everywhere, except at X equals pi. Uh, So the limit of F of X as X approaches some number A will exist for every number A except high.

Temple University