Solved by verified expert:I have uploaded file to solve the problem of limit numerically, limit Algebraically, and polynomial function with degree.
Also this question, “You start a Cake business to earn money for college. The fixed cost of this business is a$ and the variable cost is b$ per cake. You will sell each cake for $c.”
After you finish, please send me a copy of Desmos for each questions and one Word file that shows all the answers of these questions.
Thank you for helping me.
Unformatted Attachment Preview
Please, use Desmos.com to graph and to solve each problem. Use quotation to type all your answers in
Desmos.com. Print and staple your papers.
Need to show all your work to receive full credit.
1. 𝐺𝑖𝑣𝑒𝑛 𝑓(𝑥) =
𝑥 2 −𝑏
𝑓𝑜𝑟 𝑥 ≠ 𝑎
a) Find the limit numerically by completing the following.
𝑓𝑖𝑛𝑑 lim− 𝑓(𝑥) = ___________
𝑓𝑖𝑛𝑑 lim+ 𝑓(𝑥) = __________
𝑓𝑖𝑛𝑑 lim 𝑓(𝑥) = ___________
𝑏) 𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑙𝑖𝑚𝑖𝑡 𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑎𝑙𝑙𝑦. 𝐺𝑟𝑎𝑝ℎ 𝑓(𝑥). (𝑁𝑜𝑡𝑒: 𝑚𝑎𝑘𝑒 𝑠𝑢𝑟𝑒 𝑡𝑜 𝑝𝑜𝑙𝑡 𝑎 ℎ𝑜𝑙𝑒 𝑤ℎ𝑒𝑟𝑒 𝑥 = 𝑎)
c) Find the limit Algebraically (need to show your work)
𝑓𝑖𝑛𝑑 lim 𝑓(𝑥) = __________
2. You start a Cake business to earn money for college. The fixed cost of this business is a$ and the
variable cost is b$ per cake. You will sell each cake for $c.
Let x be the number of cakes sold.
a) Formulate a cost function C(x).
b) Formulate a revenue function R(x).
c) Generate a profit function P(x).
d) Find the break-even point. (how many cakes?)
e) How many cakes do you need to sell to generate a profit of $2,500?
f) Find the average profit function Avg P(x).
g) Find the derivative of Avg P(x).
h) Find the rate of change when 200 cakes are produced and sold (average profit function).
𝑀𝑎𝑘𝑒 𝑢𝑝 𝑦𝑜𝑢𝑟 𝑜𝑤𝑛 𝑝𝑜𝑙𝑦𝑛𝑜𝑚𝑖𝑎𝑙 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑤𝑖𝑡ℎ 𝑑𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 6 𝑎𝑛𝑑 𝑓𝑖𝑛𝑑
𝐹𝑜𝑟 𝑒𝑥𝑎𝑚𝑝𝑙𝑒: 𝑦 = 7𝑥 − 5𝑥 + 8𝑥
, 𝑓𝑖𝑛𝑑 3
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