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MAT 1234 Calculus I

MAT 1234 Calculus I. Section 1.5 The Limit of a Function. http://myhome.spu.edu/lauw. WebAssign. Homework 1.5 Be sure to read the instructions. What do we care?. How fast “things” are going The velocity of a particle The “speed” of formation of chemicals

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MAT 1234 Calculus I

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  1. MAT 1234Calculus I Section 1.5 The Limit of a Function http://myhome.spu.edu/lauw

  2. WebAssign • Homework 1.5 • Be sure to read the instructions.

  3. What do we care? • How fast “things” are going • The velocity of a particle • The “speed” of formation of chemicals • The rate of change of charges in a capacitor

  4. Recall • Limit of the following form is important

  5. Recall

  6. Recall

  7. Recall • Limit of the following form is important • 1.4: Estimate limits by tables • 1.6: Compute limits by algebra • 1.5: Formally define limits

  8. Preview • One-sided limits • The existence of limits • Infinite limits

  9. One-Sided Limits • We will focus on the conceptual meaning and understanding. • We will not look closely at the formal definition.

  10. Left-Hand Limit y • The left-hand limit is 2 when x approaches 3 • Notation: • Independent of f(3) 2 y=f(x) x 3

  11. Left-Hand Limit y 2 y=f(x) x 3

  12. Left-Hand Limit y 2 y=f(x) x 3

  13. Left-Hand Limit y 2 y=f(x) x 3

  14. Left-Hand Limit (Formal)

  15. Right-Hand Limit y • The right-hand limit is 4 when x approaches 2 • Notation: • Independent of f(2) 4 y=f(x) x 2

  16. Right-Hand Limit y 4 y=f(x) x 2

  17. Right-Hand Limit y 4 y=f(x) x 2

  18. Right-Hand Limit y 4 y=f(x) x 2

  19. Right-Hand Limit (Formal)

  20. Limit of a Function

  21. Example 1 y 1.5 x 2

  22. Example 2 y 2.5 1.5 x 2

  23. Infinite Limits y • The left-hand limit DNE • Notation: y=f(x) is not a number x a

  24. Infinite Limits • Let us look at all possible situations and their standard representations.

  25. Infinite Limits y • The left-hand limit DNE • Notation: x a

  26. Infinite Limits y • The right-hand limit DNE • Notation: x a

  27. Infinite Limits y • The right-hand limit DNE • Notation: x a

  28. Infinite Limits y • The limit DNE • Notation: x a

  29. Infinite Limits y • The limit DNE • Notation: x a

  30. Infinite Limits y • The limit DNE • Notation: x a

  31. Review: We learned… • left-hand and right-hand limits • definition of limits • infinite limits • infinity is a concept, not a number • to use infinity to represent geometry concepts - unboundness

  32. Classwork • Use pencils! • Work with your partner ONLY. • No discussions between groups (penalty = last group to get out) • You can go, after Tara or I check both of your work.

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