Let ff be a function of xx. The value of limx→af(x)limx→af(x) can be found using the squeeze theorem with the functions gg and hh. Which of the following could be graphs of ff, gg, and hh ?
In order to use the squeeze theorem to find the limit of ff as xx approaches aa, we need to find functions gg and hh that “squeeze” ff between them
In order to use the squeeze theorem to find the limit of ff as xx approaches aa, we need to find functions gg and hh that “squeeze” ff between them. This means that gg should be a function that is always less than or equal to ff, and hh should be a function that is always greater than or equal to ff.
To determine which of the given graphs could represent ff, gg, and hh, we need to analyze the behavior of the functions.
1. Graph A:
– This graph shows ff being squeezed between gg and hh. The function gg is always less than or equal to ff, and hh is always greater than or equal to ff. Thus, Graph A is a possible representation.
2. Graph B:
– In this graph, we can see that ff is not being squeezed between gg and hh. There are many points where ff is not between the other two functions. Therefore, Graph B is not a possible representation.
3. Graph C:
– In this graph, ff is not squeezed between gg and hh either. There are points where ff does not lie between the other two functions. So, Graph C is not a possible representation.
4. Graph D:
– Similar to the previous two graphs, this graph also does not satisfy the squeeze theorem condition. There are points where ff does not lie between the other two functions. Thus, Graph D is not a possible representation.
Based on the analysis, only Graph A could be a possible representation of the functions ff, gg, and hh.
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