Consider the Following Function $$f ( x ) = \left\{ \begin{array} { c c } 3 - x & x < - 1 \\x & - 1 \leq x < 3 \\( x - 3 ) ^ { 2 } & x \geq 3\end{array} \right.$$

question 5

Short Answer

Consider the following function. $$f ( x ) = \left\{ \begin{array} { c c } 3 - x & x < - 1 \\x & - 1 \leq x < 3 \\( x - 3 ) ^ { 2 } & x \geq 3\end{array} \right.$$
Determine the values of $a$ for which $\lim _ { x \rightarrow a } f ( x )$ exists.

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Definitions:

Protic Solvents

Solvents that have hydrogen atoms capable of forming hydrogen bonds, often used in reactions requiring proton transfer.

Alkenes

Hydrocarbons containing at least one carbon-carbon double bond, characterized by their unsaturated nature.

Reaction Products

The substances formed by the chemical change that occurs during a reaction, resulting from the rearrangement of atoms and bonds in reactants.

Mechanisms

The detailed processes or series of steps by which chemical reactions occur, explaining the breaking and making of bonds.