In a certain city the temperature (in degrees Fahrenheit) t hours after 9am was approximated by the function. How to determine the temperature at 9 am ? and How to find the average temperature during the period from 9 am to 9 pm ?

Answer 1

#68.276^@F#

The temperature at #9am# is equivalent to #T(0)#, ie #0# hours after 9am, and given by
#T(0)=60+13sin((pi(0))/12)=60^@F#.
The temperature at #9 p m # is #T(12)#, ie #12# hours after 9am, and given by
#T(12)=60+13sin((pi(12))/12)=60^@F#.

Now that we have the formula, we can use it.

#barT(t)=1/(12-0)int_0^12(60+13sin((pit)/12))dt#
#=1/12[60t-(12(13))/picos((pit)/12)]_0^12#
#=1/12[720+156/pi+156/pi]#
#=68.276^@F#
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Answer 2

To determine the temperature at 9 am, you would simply plug in (t = 0) into the given function.

To find the average temperature during the period from 9 am to 9 pm, you would integrate the given function from (t = 0) to (t = 12) (since 9 am to 9 pm covers 12 hours), and then divide the result by the total number of hours (12) to obtain the average temperature.

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Answer from HIX Tutor

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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