Expert answer:limit Algebraically & Polynomial Function with Deg


Solved by verified expert:I have uploaded file to solve the problem of limit numerically, limit Algebraically, and polynomial function with degree.Β 
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 $c.”
After you finish, please send me a copy of Desmos for each questions and one Word file that shows all the answers of these questions.
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Please, use to graph and to solve each problem. Use quotation to type all your answers in Print and staple your papers.
Need to show all your work to receive full credit.
1. 𝐺𝑖𝑣𝑒𝑛 𝑓(π‘₯) =
π‘₯ 2 βˆ’π‘
π‘“π‘œπ‘Ÿ π‘₯ β‰  π‘Ž
a) Find the limit numerically by completing the following.
𝑓𝑖𝑛𝑑 limβˆ’ 𝑓(π‘₯) = ___________
𝑓𝑖𝑛𝑑 lim+ 𝑓(π‘₯) = __________
𝑓𝑖𝑛𝑑 lim 𝑓(π‘₯) = ___________
𝑏) 𝐹𝑖𝑛𝑑 π‘‘β„Žπ‘’ π‘™π‘–π‘šπ‘–π‘‘ π‘”π‘Ÿπ‘Žπ‘β„Žπ‘–π‘π‘Žπ‘™π‘™π‘¦. πΊπ‘Ÿπ‘Žπ‘β„Ž 𝑓(π‘₯). (π‘π‘œπ‘‘π‘’: π‘šπ‘Žπ‘˜π‘’ π‘ π‘’π‘Ÿπ‘’ π‘‘π‘œ π‘π‘œπ‘™π‘‘ π‘Ž β„Žπ‘œπ‘™π‘’ π‘€β„Žπ‘’π‘Ÿπ‘’ π‘₯ = π‘Ž)
c) Find the limit Algebraically (need to show your work)
𝑓𝑖𝑛𝑑 lim 𝑓(π‘₯) = __________
Fixed Cost
Sales Price
2. You start a Cake business to earn money for college. The fixed cost of this business is a$ 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).
π‘€π‘Žπ‘˜π‘’ 𝑒𝑝 π‘¦π‘œπ‘’π‘Ÿ π‘œπ‘€π‘› π‘π‘œπ‘™π‘¦π‘›π‘œπ‘šπ‘–π‘Žπ‘™ π‘“π‘’π‘›π‘π‘‘π‘–π‘œπ‘› π‘€π‘–π‘‘β„Ž π‘‘π‘’π‘”π‘Ÿπ‘’π‘’ π‘œπ‘“ 6 π‘Žπ‘›π‘‘ 𝑓𝑖𝑛𝑑
πΉπ‘œπ‘Ÿ 𝑒π‘₯π‘Žπ‘šπ‘π‘™π‘’: 𝑦 = 7π‘₯ βˆ’ 5π‘₯ + 8π‘₯
, 𝑓𝑖𝑛𝑑 3
𝑑3 𝑦
𝑑π‘₯ 3

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