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. 5/34 Vertical Asymptotes To find vertical asymptotes look for values <strong>of</strong>xwhich make the denominator zero Example: Consider the function f(x) = 5x3 +4x−8 x 3 −2x 2 −3x Find the vertical asymptotes <strong>of</strong> f(x) Solution: Factor the denominator: x 3 −2x 2 −3x = x(x 2 −2x−3) = x(x−3)(x+1) So vertical asymptotes are: x = 0,x = 3, x = −1
– p. 6/34 Horizontal Asymptotes To find horizontal asymptotes
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Page 3 and 4: - p. 2/34 Asymptotes A nonvertical
Page 11 and 12: - p. 3/34 Example Lety = f(x) = x+
Page 13 and 14: Example Lety = f(x) = x+ 1 x f ′
Page 23 and 24: - p. 4/34 Graph of x+1/x ♣ (1,2)
Page 25 and 26: Graph of x+1/x 1 lim x→0 + x =
Page 27 and 28: - p. 4/34 Graph of x+1/x 1 lim x→
Page 29 and 30: - p. 4/34 Graph of x+1/x 1 lim x→
Page 31 and 32: - p. 5/34 Vertical Asymptotes To fi
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Page 43 and 44: - p. 6/34 Horizontal Asymptotes To
Page 47 and 48: Horizontal Asymptotes To find horiz
Page 49 and 50: Horizontal Asymptotes To find horiz
Page 55 and 56: - p. 7/34 Computing Limits When fin
Page 61 and 62: - p. 8/34 Example 1. Compute the li
Page 63 and 64: Example 1. Compute the limit x 2 +8
Page 65 and 66: - p. 8/34 Example 1. Compute the li
Page 67 and 68: - p. 9/34 Second example This limit
Page 69 and 70: Second example This limit may end u
Page 71 and 72: - p. 9/34 Second example This limit
Page 73 and 74: - p. 10/34 Graphs with asymptotes S
Page 75 and 76: Graphs with asymptotes Sketch the g
Page 77 and 78: Graphs with asymptotes Sketch the g
Page 79 and 80: - p. 11/34 Graphs continued Since t
Page 81 and 82: Graphs continued Since the first de
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Page 85 and 86: - p. 11/34 Graphs continued Since t
Page 87 and 88: - p. 12/34 Find the Asymptotes For
Page 89 and 90: Find the Asymptotes For y = f(x) =
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Find the Asymptotes For y = f(x) =
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- p. 12/34 Find the Asymptotes For
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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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