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Math 140 Calculus for Business

  • If you are considering taking a lower-level class than Math 140:
    • We encourage you to consider taking the corequisite course—Math 14—which provides additional support for Math 140.
    • The next level lower is Math 130 (College Algebra).
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  • Sample of what you should know before taking Math 140:
    1. Suppose F of x equals x squared minus 2 x. Find F of open parenthesis start fraction 1 over x plus 1 end fraction close parenthesis and simplify
    2. Find all asymptotes and intercepts of F of x equals start fraction 2 x over x squared minus 1 end fraction
      • Solution
        Vertical asymptotes: x squared minus 1 equals 0 therefore x equals 1 or x equals negative 1
        Horizontal asymptote:
        y equals 2 over 1 therefore y equals 2
        x-intercept:
        start fraction 2 x over x squared minus 1 end fraction equals 0 therefore 2 x equals 0 therefore x equals 0
        y-intercept:
        f of open parenthesis 0 close parenthesis equals start fraction 2 times 0 over 0 squared minus 1 end fraction equals 0
    3. Find all rational zeros of f of x equals 6 x to the fourth plus 7 x cubed minus 12 x squared minus 3 x plus 2 and factor into linear factors.
    4. Simplify start fraction start fraction 1 over x plus h end fraction minus start fraction 1 over x end fraction over h end fraction
    5. Solve4 plus 10 e superscript negative 4 x baseline equals 6
  • Sample of what you will learn in Math 140:
    1. Evaluatelimit as x goes to 1 from the left of start fraction x minus start square root x end square root over x minus 1 end fraction
    2. The total cost of buying books is capital C of x equals 24 x superscript 2 thirds dollars. At what rate is the total cost changing when 64 books are purchased?
      • Solution
        capital c prime of x equals 16 x superscript negative 1 third
        capital c prime open parenthesis 64 close parenthesis equals 16 times 64 superscript negative 1 third baseline equals 4
        The total cost is changing at a rate of dollars per book.
    3. Use calculus to analyze and graph F of x equals x squared e superscript negative x
    4. Suppose a demand curve (in dollars per unit) is capital D open parenthesis q close parenthesis equals 75 e superscript negative 0 point 0 3 q   . Find the price at which 4 units will be demanded, and then compute the consumer surplus at that price.
    5. Find the critical points of f open parenthesis x comma y close parenthesis equals 12 x minus x cubed minus 4 y squared and classify each as a relative maximum, a relative minimum, or a saddle point.
      • Solution
        f subscript x baseline equals 12 minus 3 x squared comma f subscript y baseline equals negative 8 y comma f subscript x x baseline equals negative 6 x comma f subscript y y baseline equals negative 8 comma f subscript x y baseline equals 0
        capital D open parenthesis x comma y close parenthesis equals open parenthesis negative 6 x close parenthesis open parenthesis negative 8 close parenthesis minus 0 squared equals 48 x
        12 minus 3 x squared equals 0 therefore x equals plus or minus 2
        negative 8 y equals 0 therefore y equals 0
        critical points are 2 comma 0 and negative 2 comma 0
        capital D open parenthesis 2 comma 0 close parenthesis equals 48 times 2 equals 96 is greater than 0 and f subscript x x baseline open parenthesis 2 comma 0 close parenthesis equals negative 6 times 2 equals negative 12 is less than 0
        so (2, 0) is a relative maximum.
        capital d open parenthesis negative 2 comma 0 close parenthesis equals 48 times negative 2 equals negative 96 is less than 0 so (-2, 0) is a saddle point.