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Calculus I (Assignment Problems) / Limits / The Limit   [Notes] [Practice Problems] [Assignment Problems]

Calculus I - Assignment Problems
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 The Limit

 

1. For the function  answer each of the following questions.

(a) Evaluate the function the following values of x compute (accurate to at least 8 decimal places).

(i) -2.5              (ii) -2.9             (iii) -2.99            (iv) -2.999          (v) -2.9999

(vi) -3.5            (vii) -3.1           (viii) -3.01          (ix) -3.001          (x) -3.0001

(b) Use the information from (a) to estimate the value of .

 

2. For the function  answer each of the following questions.

(a) Evaluate the function the following values of t compute (accurate to at least 8 decimal places).

(i) 1.5              (ii) 1.1             (iii) 1.01            (iv) 1.001          (v) 1.0001

(vi) 0.5            (vii) 0.9           (viii) 0.99          (ix) 0.999          (x) 0.9999

(b) Use the information from (a) to estimate the value of .

 

3. For the function  answer each of the following questions.

(a) Evaluate the function the following values of  compute (accurate to at least 8 decimal places).  Make sure your calculator is set to radians for the computations.

(i) 0.5               (ii) 0.1              (iii) 0.01              (iv) 0.001           (v) 0.0001

(vi) -0.5            (vii) -0.1           (viii) -0.01          (ix) -0.001          (x) -0.0001

(b) Use the information from (a) to estimate the value of .

 

4. For the function  answer each of the following questions.

(a) Evaluate the function the following values of  compute (accurate to at least 8 decimal places).  Make sure your calculator is set to radians for the computations.

(i) 4.5              (ii) 4.1             (iii) 4.01            (iv) 4.001          (v) 4.0001

(vi) 3.5            (vii) 3.9           (viii) 3.99          (ix) 3.999          (x) 3.9999

(b) Use the information from (a) to estimate the value of .

 

5. Below is the graph of .  For each of the given points determine the value of  and .  If any of the quantities do not exist clearly explain why.

 

(a)                       (b)                       (c)                       (d)  

TheLimit_Ex5

 

6. Below is the graph of .  For each of the given points determine the value of  and .  If any of the quantities do not exist clearly explain why.

 

(a)                       (b)                       (c)                       (d)  

TheLimit_Ex6

 

7. Below is the graph of .  For each of the given points determine the value of  and .  If any of the quantities do not exist clearly explain why.

 

(a)                       (b)                       (c)                       (d)  

TheLimit_Ex7

 

8. Explain in your own words what the following equation means.

 

 

 

9. Suppose we know that .  If possible, determine the value  .  If it is not possible to determine the value explain why not.

 

10.  Is it possible to have  and ?  Explain your answer.

 

Tangent Lines and Rates of Change Previous Section   Next Section One-Sided Limits
Review Previous Chapter   Next Chapter Derivatives

Calculus I (Assignment Problems) / Limits / The Limit    [Notes] [Practice Problems] [Assignment Problems]

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