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Groupwork 2
1. Given the following function of f (x)
(a) Find
(b) Find
(9pts)
lim f (x)
x→−2−
lim f (x)
x→−2+
(c) Find lim f (x)
x→−2
(d) Is f (x) Continous at x = 1? If not which rule of continuity do we fail?
(e) Find
lim
x→−1
3f (x)2
2. given the following functions for cost and revenue, where x represents millions of units
R(x) = −29x2 + 709x
C(x) = 224x + 25
(a) Find a function for the profit P (x)
(b) Between what units will a profit be made?
(c) Find the max profit
3. A colony of bats starts with a population of 1500. If they grow 3.5% continuously each
month, how long will it take them to reach a population of 4000 bats?
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Explanation & Answer
Attached.
1.
a)
Revenue (𝑅(𝑥)) is price (𝑝(𝑥)) times the number of units sold (𝑥):
𝑅(𝑥) = 𝑝 ∙ 𝑥
𝑅(𝑥) = 𝑥 ∙ (75 − 1.3 ∙ 𝑥)
𝑅(𝑥) = 75𝑥 − 1.3𝑥 2
b)
Profit(𝑃(𝑥)) is revenue minus the cost (𝐶(𝑥)):
𝑃(𝑥) = 𝑅(𝑥) − 𝐶(𝑥)
𝑃(𝑥) = 75𝑥 − 1.3𝑥 2 − (300 + 0.75𝑥)
𝑃(𝑥) = −1.3𝑥 2 + 74.25𝑥 − 300
c)
For a second o...
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