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Lecture Notes for MATH 1300 - Analytic Geometry and Calculus 1 at Colorado (CU)

Notes Information

Material Type:Review Sheet
Professor:Staff
Class:MATH 1300 - Analytic Geometry and Calculus 1
Subject:Mathematics
University:University of Colorado - Boulder
Term:Fall 2006
Keywords:
  • Assumptions
  • Differentiable
  • Trigonometric
  • Vertical Tangent Line
  • Relative Maximum
  • Discontinuous
  • Inflection Point
  • Critical Points
  • Rational Function
  • Open Interval
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Sample Document Text

Math 1300: Calculus I, Fall 2006 Answer Sheet for Review 3 1. Your graph should look something like this: 2. No, limx?0 fprime(x)gprime(x) does not exist. 3. 11.5 and 11.5 4. Answer: 16. 5. (a) nsummationdisplay k=0 parenleftbigg 1 2k parenrightbigg3 = nsummationdisplay k=0 1 8k (b) lim n?? 8(8n ?1/8) 7(8n) = 8 7 cm 3 6. Solution: (1) Increasing: (??,?2]?[0,?) Decreasing: [?2,0] (2) Relative Maximum: (?2,4e?2) Relative Minimum: (0,0) (3) Concave Up: (??,?2??2)?(?2 +?2,+?) Concave Down: (?2??2,?2 +?2) Inflection Points: x = ?2?2 1 2 7. f(x) attains its minimum of 1 at x = 0. By the definition of an absolute minimum, f(x) ? 1 > 0 for all x. The desired inequality follows directly from this. 8. To prove the first statement in the Hint, suppose that the graph of f has a point P = (b,f(b)) with b in I such that P lies below or on the tangent line lscript and a < b. Then f(b)?f(a) b?a ? (the slope of lscript) = f prime(a). Since f is differentiable on the open interval I an...

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