Loading Solution   
Paul's Online Math Notes
Calculus I (Practice Problems) / Limits / The Limit   [Notes] [Practice Problems] [Assignment Problems]

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

 

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) 2.1             (iii) 2.01            (iv) 2.001          (v) 2.0001

(vi) 1.5            (vii) 1.9           (viii) 1.99          (ix) 1.999          (x) 1.9999

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

[Solution]

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) -0.5              (ii) -0.9             (iii) -0.99            (iv) -0.999          (v) -0.9999

(vi) -1.5            (vii) -1.1           (viii) -1.01          (ix) -1.001          (x) -1.0001

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

[Solution]

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 .

[Solution]

4. 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_Ex4

[Solution]

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

[Solution]

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

[Solution]

 

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

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

© 2003 - 2017 Paul Dawkins