Math 211 Business Calculus Applications of Derivatives

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$Math 229 Summation Worksheet$

$Math 211 Business Calculus - Department of Mathematical Sciences ...$

$Math 230 Practice Exam 1 Solutions$

$Math 210 Lecture Notes - Department of Mathematical Sciences ...$

– p. 3/34 Example Lety = f(x) = x+ 1 x f ′ (x) = 1− 1 x 2 = 1−x −2 f ′′ (x) = 2x −3 = 2 x 3 Since lim f(x) = lim 1 x→0 + x→0 +x+ x = ∞ x = 0 (they-axis) is a vertical asymptote. Since lim x→∞ f(x)−x
– p. 3/34 Example Lety = f(x) = x+ 1 x f ′ (x) = 1− 1 x 2 = 1−x −2 f ′′ (x) = 2x −3 = 2 x 3 Since lim f(x) = lim 1 x→0 + x→0 +x+ x = ∞ x = 0 (they-axis) is a vertical asymptote. 1 Since lim f(x)−x = lim x→∞ x→∞ x
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Page 3 and 4: - p. 2/34 Asymptotes A nonvertical
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Page 13 and 14: Example Lety = f(x) = x+ 1 x f ′
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Page 23 and 24: - p. 4/34 Graph of x+1/x ♣ (1,2)
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Page 27 and 28: - p. 4/34 Graph of x+1/x 1 lim x→
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Page 31 and 32: - p. 5/34 Vertical Asymptotes To fi
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Page 55 and 56: - p. 7/34 Computing Limits When fin
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Page 63 and 64: Example 1. Compute the limit x 2 +8
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Second example This limit may end u
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- p. 9/34 Second example This limit
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- p. 10/34 Graphs with asymptotes S
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Graphs with asymptotes Sketch the g
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Graphs with asymptotes Sketch the g
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- p. 11/34 Graphs continued Since t
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Graphs continued Since the first de
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Graphs continued Since the first de
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- p. 11/34 Graphs continued Since t
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- p. 12/34 Find the Asymptotes For
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Find the Asymptotes For y = f(x) =
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Find the Asymptotes For y = f(x) =
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Graph of (x−2)/(x+1) - p. 13/34
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- p. 13/34 Graph of (x−2)/(x+1) x
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- p. 13/34 Graph of (x−2)/(x+1) x
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- p. 13/34 Graph of (x−2)/(x+1) x
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- p. 14/34 Business Applications Th
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- p. 16/34 Maximize Revenue If the
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- p. 17/34 Max versus Min R = −0.
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- p. 18/34 Maximize Revenue The rev
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- p. 19/34 Max versus Min R = x 3
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- p. 20/34 Maximize Profit As a gen
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- p. 21/34 Maximize Profit Example
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What level of sales maximizes profi
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- p. 22/34 Ticket Sales Problem •
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- p. 23/34 Ticket Sales Setup Letx=
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- p. 24/34 Ticket Sales Solution R(
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- p. 25/34 Dog Kennel Problem The o
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- p. 26/34 Dog Kennel Setup Letx=le
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- p. 27/34 Dog Kennel Solution Solv
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- p. 28/34 Another Fencing Problem
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Another Fencing Problem The owner o
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- p. 29/34 Fencing Problem Setup Le
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- p. 30/34 Fence Solution Solve xy
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Fence Solution Solve xy = 810 fory:
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- p. 31/34 Limit Def Revisited Reca
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- p. 32/34 Marginal Revenue, Profit
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- p. 33/34 Marginal Example Flying
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- p. 34/34 Marginal Example Continu
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Math 211 Business Calculus Applications of Derivatives

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