2. Limits and Continuity 1
1.1
A BRIEF PREVIEW OF CALCULUS: TANGENT LINES AND THE LENGTH OF A CURVE
1.2
THE CONCEPT OF LIMIT
1.3
COMPUTATION OF LIMITS
1.4
CONTINUITY AND ITS CONSEQUENCES
1.5
LIMITS INVOLVING INFINITY; ASYMPTOTES
1.6
FORMAL DEFINITION OF THE LIMIT
1.7
LIMITS AND LOSS OF SIGNIFICANCE ERRORS
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3. 1.3 COMPUTATION OF LIMITS For any constant c and any real number a,
For any real number a,
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4. 1.3 COMPUTATION OF LIMITS 3.1 Slide 4
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5. 1.3 COMPUTATION OF LIMITS 3.1 Finding the Limit of a Polynomial
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6. 1.3 COMPUTATION OF LIMITS 3.1 Finding the Limit of a Polynomial
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7. 1.3 COMPUTATION OF LIMITS 3.3 Finding a Limit by Factoring Slide 8
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8. 1.3 COMPUTATION OF LIMITS 3.3 Finding a Limit by Factoring
Notice right away that
since the limit in the denominator is zero.
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9. 1.3 COMPUTATION OF LIMITS 3.3 Finding a Limit by Factoring Slide 10
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10. 1.3 COMPUTATION OF LIMITS 3.2 Slide 10
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11. 1.3 COMPUTATION OF LIMITS 3.3 Slide 11
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12. 1.3
COMPUTATION OF LIMITS
3.4
Evaluating the Limit of an nth Root of a Polynomial
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13. 1.3
COMPUTATION OF LIMITS
3.4
Evaluating the Limit of an nth Root of a Polynomial
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14. 1.3 COMPUTATION OF LIMITS 3.5 Finding a Limit by Rationalizing
Notice that both the numerator and the denominator approach 0 as x approaches 0.
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15. 1.3 COMPUTATION OF LIMITS 3.5 Finding a Limit by Rationalizing
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16. 1.3 COMPUTATION OF LIMITS 3.5 Finding a Limit by Rationalizing
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17. 1.3 COMPUTATION OF LIMITS 3.4 Slide 17
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18. 1.3 COMPUTATION OF LIMITS 3.5 (Squeeze Theorem) Slide 18
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19. 1.3
COMPUTATION OF LIMITS
3.8
Using the Squeeze Theorem to Verify the Value of a Limit
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20. 1.3
COMPUTATION OF LIMITS
3.8
Using the Squeeze Theorem to Verify the Value of a Limit
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21. 1.3
COMPUTATION OF LIMITS
3.8
Using the Squeeze Theorem to Verify the Value of a Limit
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22. 1.3 COMPUTATION OF LIMITS 3.9 A Limit for a Piecewise-Defined Function
(Consider one-sided limits.)
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23. 1.3 COMPUTATION OF LIMITS 3.9 A Limit for a Piecewise-Defined Function
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