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 ?
To use the squeeze theorem, we need to find two functions gg and hh such that ff is squeezed between them as x approaches a
To use the squeeze theorem, we need to find two functions gg and hh such that ff is squeezed between them as x approaches a. This means that the graph of ff should lie between the graphs of gg and hh near the point a.
Here are three scenarios that could satisfy the given conditions:
Scenario 1:
ff: A function that is increasing as x approaches a. The graph of ff is “sandwiched” between the graphs of gg and hh, with gg lying below ff and hh lying above ff.
Scenario 2:
ff: A function that is decreasing as x approaches a. The graph of ff is “sandwiched” between the graphs of gg and hh, with gg lying above ff and hh lying below ff.
Scenario 3:
ff: A constant function. The graph of ff is “sandwiched” between the horizontal lines defined by the graphs of gg and hh.
Note that these scenarios are just examples and there may be other possible combinations of functions gg and hh that satisfy the given conditions.
To determine the specific graphs of ff, gg, and hh, we would need more information or further constraints.
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