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Calculus I (MAT 145) Dr. Day Thur sday Feb 7, 2013

Calculus I (MAT 145) Dr. Day Thur sday Feb 7, 2013. Limits Involving Infinity (2.6) Continuity of a Function (2.5) Assignments. What About Limits? (2.1-2.3; 2.6; PIP pp 14-17; 20). Concept of a Limit: Approachment Symbolizing Limits Determining Limits Properties of Limits

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Calculus I (MAT 145) Dr. Day Thur sday Feb 7, 2013

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  1. Calculus I (MAT 145)Dr. Day Thursday Feb 7, 2013 • Limits Involving Infinity (2.6) • Continuity of a Function (2.5) • Assignments MAT 145

  2. What About Limits?(2.1-2.3; 2.6; PIP pp 14-17; 20) • Concept of a Limit: Approachment • Symbolizing Limits • Determining Limits • Properties of Limits • Limits Involving Infinity MAT 145

  3. Approachment • What patterns of approachment in outputs are apparent when the inputs approach some value? • Reminder! We’re not concerned with behavior AT the specific point, only the behavior that’s apparent as we approach it! • Numerical, Graphical, and Symbolic Perspectives • One-Sided and Two-Sided Limits MAT 145

  4. MAT 145

  5. How can we use limit notation to describe the “approachment” exhibited in this graph of inputs and outputs? MAT 145

  6. Use limit symbolism to describe both the one-sided and the two-sided limits that seem apparent as x approaches 0 in the top graph and as x approaches 3 in the other graph. If a particular limit does not exist, signify that with DNE. MAT 145

  7. LimitsInvolving Infinity Limits Involving Infinity (PIP p 20) • Horizontal and Vertical Asymptotes • Special Cases: Rational Functions MAT 145

  8. What Makes a Function Continuous? (PIP pp 18-19) Informal Perspective Formal Definition One-Sided Continuity Continuity on an Interval Connections: Limits and Continuity MAT 145

  9. MAT 145

  10. MAT 145

  11. Assignments • WebAssign • 2.2 due tonight • 2.3 due tonight • 2.6 due tomorrow night Test #2: Friday, February 15 MAT 145

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