My s Answers SCalcET8 2.5.010. Which of the following are continuous functions?
ID: 2890204 • Letter: M
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My s Answers SCalcET8 2.5.010. Which of the following are continuous functions? (Select all that apply.) O The temperature at a specific location as a function of time. The temperature at a specific time as a function of the distance due west from New York City. The altitude above sea level as a function of the distance due west from New York City The cost of a taxi ride as a function of the distance traveled. O The current in the circuit for the lights in a room as a function of time. O None of these. Enhanced Feedback Please try again. Remember, in order for a function to be continuous, the value of the function must change inpu values. t varies. Therefore the value of the function can't jump from one value to another without passing throExplanation / Answer
a> The temperature at a specific location as a function of time.
This is a continuous function as the temperature cannot abruptly change from one value of another without passing through the values in between. In other words this function cannot make significant changes without being continuous.
b> The temperature at a specific time as a function of the distance due west from New York city.
This is a continuous function as we are again dealing with a temperature function and from the above discussion we could say that temperature cannot change in a fraction of time.
Here as the temperature is a function of distance. So the temperature of a particular place will be accordingly to the temperature of the nearby places.Hence its continuous.
c> The altitude above sea level as a function of the distance due west from New York City.
This is a discontinuous function
In a sea there are rocks that often project above the water level and are visible as well. So we coiuld say that the sea does not have water at all the levels. So where ever there are pointy rocks projecting above the sea level at such points this function will not be defined and hence discontinuous.
d> The cost of a taxi ride as a function of the distance travelled.
This is a discontinuous functon as the taxi fare veries according taxi meter's reading .
The taxi meter decides the cost as the meter runs even when the taxi is at the signal and not moving.
e> The currect in the circuit for the lights in a room as a function of time.
This is a discontinuous function.
As when there is a power cut or we switch off the lights there is no currect in the circuit. So the time does not decide whether the currect is in the circuit or not.
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