Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A printer charges a set-up fee of rupees plus rupees for each book. For books, the average cost per book is rupees per book. Find the average cost per book for books and for books. Then find the value that the average cost approaches as the number of books grows without bound.
When substitution gives , factorise or rationalise, cancel the common factor, and substitute again. For divide the top and the bottom by the highest power of , and use .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. in rupees per book.
Plan. Substitute for the two values of , then divide the top and the bottom by for the limit.
Step 1. For 100 books. rupees per book.
Step 2. For 1000 books. rupees per book.
Step 3. The limit. Divide the top and the bottom by : . As , , so rupees per book.
Check. The set-up fee is shared among more and more books, so the cost per book falls towards the cost of printing one book, rupees.
Answer: and rupees per book, and the limit is rupees per book.
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