Which of the following are equivalent
1 answer:
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Answer:
80 movies must be streamed.
Step-by-step explanation:
To find the average cost, you must divide the total cost by the number of movies watched.
When you watch 1 movie, you pay the initial fee of $80 plus a $4 purchase of the film.
The equation is shown as such:
average cost = (total cost)/(number of movies)
Your total cost can be represented as , while the number of movies is represented as
.
You want the average to equal 5, so your equation is shown as follows:
simplifying this, we get
which can then be simplified to
X = 80 movies.
By inspection, it's clear that the sequence must converge to 
because
when
is arbitrarily large.
Now, for the limit as
to be equal to is to say that for any 
, there exists some 
such that whenever 
, it follows that
From this inequality, we get
As we're considering, we can omit the first inequality.
We can then see that choosing
will guarantee the condition for the limit to exist. We take the ceiling (least integer larger than the given bound) just so that 
.
when
Now, for the limit as
From this inequality, we get
As we're considering
We can then see that choosing