LIMITS UNIT PROBLEM SETS

PROBLEM SET #1 – Tangent Lines***Calculators Not Allowed***

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  1. Given: Find the slope of the tangent lineat
  1. Given: Find the slope of the secant line betweenand
  1. Given: Find the equation of the tangent line at
  1. Given: Find the slope of the tangent line at
  1. Given: Find the slope of the secant line between and
  1. Given: Find the equation of the tangent line at
  1. Given: Find the slope of the tangent line at
  1. Given: Find the slope of the secant line betweenand
  1. Given: Find the equation of the tangent line at
  1. Given: Find the slope of the tangent line at

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PROBLEM SET #2 –Limits (Graphs)***Calculators Not Allowed***

For problems #1-8, find the limit of the function at the given point:



Use for problems #1-4



Use for problems #5-8

PROBLEM SET #3 –Computing Limits***Calculators Not Allowed***

For the following, find the limit of the function at the given point:

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PROBLEM SET #4 –Indeterminate Form***Calculators Not Allowed***

Evaluate the following limits:

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PROBLEM SET #5 –Infinite Limits***Calculators Not Allowed***

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Use a graphical or number line approach to evaluate the following limits:

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PROBLEM SET #6 –Piecewise Defined Limits***Calculators Not Allowed***

Evaluate the following limits using the given piecewise functions:

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PROBLEM SET #7 –End Behaviors***Calculators Not Allowed***

Evaluate the following limits:

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PROBLEM SET #8 –Trig Limits***Calculators Not Allowed***

Evaluate the following limits:

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PROBLEM SET #9 –Difference Quotient***Calculators Not Allowed**

Use the difference quotient to answer the following questions.

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1. Calculate the slope of the tangent line to at .

2. Calculate the slope of the tangent line to at .

3. Calculate the slope of the tangent line to at .

4. Calculate the slope of the tangent line to at any value x.

5. Calculate the slope of the tangent line to at .

6. Calculate the slope of the tangent line to at .

7. Calculate the slope of the tangent line to at .

8. Calculate the slope of the tangent line to at any value x.

9. Calculate the slope of the tangent line to at .

10. Calculate the slope of the tangent line to at .

11. Calculate the slope of the tangent line to at any value x.

12. Calculate the slope of the tangent line to at .

13. Calculate the slope of the tangent line to at .

14. ** Calculate the slope of the tangent line to at .

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Limits and Continuity- Answer Keys

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Problem Set #1 – Tangent Lines

  1. 2
  2. -4
  3. or
  4. 5
  5. 1
  6. 0
  7. 2/3
  8. or
  9. 1/4

Problem Set #2– Limits (Graphs)

  1. 0
  2. DNE
  3. 1.25
  4. 1
  5. 4 or
  6. 0
  7. 1
  8. -0.75

Problem Set #3 – Computing Limits

  1. 4
  2. 0
  3. -6
  4. 0
  5. 1
  6. ln(3)+1
  7. 3
  8. 0
  9. DNE
  10. 0
  11. 30
  12. 0
  13. DNE
  14. 2
  15. DNE

Problem Set #4 – Indeterminate Form

  1. 7
  2. -6
  3. 0
  4. -14
  5. 10
  6. 1
  7. 2
  8. -2
  9. 1
  10. 2
  11. 0
  12. 8
  13. 1
  14. 10
  15. 9

Problem Set #5 – Infinite Limits

  1. -
  2. +
  3. DNE
  4. +
  5. +
  6. +
  7. DNE
  8. +
  9. -
  10. DNE
  11. +
  12. DNE

Problem Set #6– PiecewiseLimits

  1. 1
  2. -5
  3. -2
  4. -4
  5. 0
  6. DNE
  7. 0
  8. 1/2
  9. 1/3
  10. 1
  11. 1
  12. 1/11
  13. 0
  14. 1
  15. DNE

Problem Set #7 – End Behaviors

  1. 0
  2. 1
  3. -1
  4. 4/7
  5. 1
  6. 0
  7. 0
  8. 0
  9. 0
  10. -3
  11. 0
  12. 1/2
  13. -1/2
  14. 2/3
  15. 2/3
  16. 0
  17. 0

Problem Set #8 – Trig Lines

  1. 2
  2. 0
  3. 1
  4. 5/7
  5. 0
  6. 4
  7. 1
  8. 16
  9. 1
  10. 0
  11. 0
  12. 1
  13. 0
  14. 4
  15. 2

Problem Set #9 – Difference Quotient

  1. 0
  2. -8
  3. 2
  4. 3x2
  5. 24
  6. -1
  7. 2
  8. 0
  9. -1/36
  10. -2
  11. 1/6
  12. 1
  13. 1/7

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