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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 $} \end{array} \right.$
05:40
Daniel J.
0:00
Anjali K.
Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 2
The Limit of a Function
Limits
Derivatives
Ali L.
October 12, 2020
Oregon State University
Harvey Mudd College
University of Nottingham
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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.
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