The function f(t) = 5 cos(pi over 6t) + 7 represents the tide in Stanley Sea. It has a maximum of 12 feet when time (t) is 0 and
a minimum of 2 feet. The sea repeats this cycle every 12 hours. After four hours, how high is the tide?
11.3 feet
9.5 feet
4.5 feet
2.6 feet
11.3 feet
9.5 feet
4.5 feet
2.6 feet
2 answers:
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Answer:
1) -95.
2) 15.
3) The conference center is on floor 5.
Step-by-step explanation:
1) Evaluating gives
2) Substituting gives
3) After going 4 floors down, we are on level -4. After going 9 floors up to the desired room, we are on level -4+9=5. So the conference center is on floor 5.
By first principles, the derivative is
Use the binomial theorem to expand the numerator:
where
The first term is eliminated, and the limit is
A power of in every term of the numerator cancels with
in the denominator:
Finally, each term containing approaches 0 as
, and the derivative is