Use the graph of f to state the value of each quantity, if it exists. If it does not exist, explain why. a) `lim_(x->2-) f(x)` b) `lim_(x->2+) f(x)` c) `lim_(x->2) f(x)` d) f(2) e) `lim_(x->4) f(x)` f) f(4)
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The graph of the function that is given can be used to determine all the required values in the question.
1. `lim_(x->2-) f(x)`
`lim_a- f(x)` refers to the value of f(a) as x approaches a from values smaller than a. In the graph, it refers to the value of f(a) as we move toward "a" from the left hand side.
The graph of the function is not continuous at 2.
If we move toward 2 from the left hand side, the value of f(2) is 3. In the graph, there is a closed dot at f(2), and it lies at (2, 3), as we move from the left. Therefore `lim_(x->2-) f(x) = 3`
2. `lim_(x->2+) f(x)`
`lim_(x->a+) f(x)` refers to the value of f(a) as x approaches "a" from values greater than "a." In the graph, it refers to the value of f(a), as we move toward "a" from the right hand side.
If we move toward x = 2 from the right hand side, there is an open dot at f(2). Though the value of f(2) in this part of the graph is not defined, the value of `lim_(x->2+) f(x)` can be determined. This is equal to 1.
f(2)The value of...
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