h(t)= cot(t) [(3.14)/(4), ((3)(3.14)/(4))] Find the average rate of change of the function over the giveninterval or intervals.

Bernard Boyer 2022-07-27 Answered
h ( t ) = cot ( t )
[(3.14)/(4), ((3)(3.14)/(4))]
Find the average rate of change of the function over the given interval or intervals.
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Answers (2)

thenurssoullu
Answered 2022-07-28 Author has 13 answers
The formula the poster listed above is used to find the averagefunction value...not the average rate of change.
the average rate change of f(x) from a to b is f ( b ) f ( a ) b a
so in this case a = π / 4   a n d   b = 3 π / 4 then.
h ( 3 π 4 ) h ( π 4 ) 3 π 4 π 4 = cot 3 π 4 cot π 4 π 2 = 2 π ( cos 3 π 4 sin 3 π 4 cos π 4 sin π 4 ) = 2 π ( 2 2 2 2 2 2 2 2 ) = 2 π ( 1 1 )
= 4 π
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posader86
Answered 2022-07-29 Author has 3 answers
average rate of change means:
1 t 2 t 1 t 1 t 2 d d t cot ( t ) d t
Which is just:
( cot ( t 2 ) cot ( t 1 ) ) / ( t 2 t 1 )
Here we have
t 1 = π / 4
t 2 = 3 π / 4
So the average is:
( cot ( 3 π / 4 ) cot ( π / 4 ) ) / ( π / 2 )
= ( 1 1 ) / ( π / 2 ) = 4 / π
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