L’Hôpital’s Rule

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• Misc
  • Math colloquia
    • Leary, “Axioms, Models, Infinity, and the Nature of the Universe”
      • Thursday, Feb. 5, 2:30 - 3:30, Newton 203
    • Dickerson, “Mathematics Majors’ Understandings of the Concept of Mathematical Definition”
      • Monday, Feb. 9 4:00 - 5:00, Newton 201 (Note corrected time)
    • Extra credit for going and writing summary/reaction to either or both
• Questions?
  • x^ln2 same as 2^lnx?
    • Take logs to remove exponential
    • Or realize that x = e^lnx, 2 = e^ln2
• L’Hôpital’s Rule
  • Section 7.5
    • lim_x→a( f(x)/g(x) ) = lim_x→a( f′(x)/g′(x) ) if f(a) = g(a) = 0 or f(a) and g(a) infinite
    • Can cascade
    • “Indeterminate form” = expression with no evaluation rules, and/or where rules break down
      • 0/0, ∞/∞, ∞ - ∞, …
  • Examples
    • lim_x→0(x²/x)
      
      • Beware that L’Hôpital’s rule doesn’t always apply at all
    • lim_x→0( 3 tanx/x )
      
      • Notice that previous limit rules, e.g., constant multiple rule, still apply and can sometimes be helpful
    • lim_x→0+( (1+2/x)^x )
      
• Problem Set
  • Handout
• Next
  • Finish L’Hôpital example with logarithm
  • Introduction to methods of integration
  • Section 8.1

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