In the following graph, how do you determine the value of c such that #lim_(x->c) f(x)# exists?
show below
show below:
For the function in the graph below f(x) is defined when x = -2 but the value which f(x) will approach as x gets closer to -3 from the left is different from the value that it will approach as x gets closer to -3 from the right.
Looking at the graph we can see that as x approaches -3 from the left f(x) approaches (negative two) however as x approaches -3 from the right f(x) approaches (negative three).
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To determine the value of c such that lim_(x→c) f(x) exists, you need to observe the behavior of the function f(x) as x approaches c from both sides. If the function approaches the same value from both the left and right sides as x approaches c, then lim_(x→c) f(x) exists and is equal to that common value.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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