Exam 2: Section 4: Limits and Their Properties

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Find all values of c such that Find all values of c such that   is continuous on   .  is continuous on Find all values of c such that   is continuous on   .  . Find all values of c such that   is continuous on   .

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E

Find the value of c guaranteed by the Intermediate Value Theorem. Find the value of c guaranteed by the Intermediate Value Theorem.

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D

Use the graph as shown to determine the following limits, and discuss the continuity of the function at Use the graph as shown to determine the following limits, and discuss the continuity of the function at   . (i)   (ii)   (iii)    . (i) Use the graph as shown to determine the following limits, and discuss the continuity of the function at   . (i)   (ii)   (iii)    (ii) Use the graph as shown to determine the following limits, and discuss the continuity of the function at   . (i)   (ii)   (iii)    (iii) Use the graph as shown to determine the following limits, and discuss the continuity of the function at   . (i)   (ii)   (iii)    Use the graph as shown to determine the following limits, and discuss the continuity of the function at   . (i)   (ii)   (iii)

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A

Find the limit (if it exists). Find the limit (if it exists).

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Find the value of c guaranteed by the Intermediate Value Theorem. Find the value of c guaranteed by the Intermediate Value Theorem.

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Use the graph as shown to determine the following limits, and discuss the continuity of the function at Use the graph as shown to determine the following limits, and discuss the continuity of the function at   . (i)   (ii)   (iii)    . (i) Use the graph as shown to determine the following limits, and discuss the continuity of the function at   . (i)   (ii)   (iii)    (ii) Use the graph as shown to determine the following limits, and discuss the continuity of the function at   . (i)   (ii)   (iii)    (iii) Use the graph as shown to determine the following limits, and discuss the continuity of the function at   . (i)   (ii)   (iii)    Use the graph as shown to determine the following limits, and discuss the continuity of the function at   . (i)   (ii)   (iii)

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Find the limit (if it exists). Note that Find the limit (if it exists). Note that   represents the greatest integer function.  represents the greatest integer function. Find the limit (if it exists). Note that   represents the greatest integer function.

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Discuss the continuity of the function Discuss the continuity of the function   .  . Discuss the continuity of the function   .

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Find the limit (if it exists). Find the limit (if it exists).

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Find the x-values (if any) at which Find the x-values (if any) at which   is not continuous. is not continuous.

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Find the constant a such that the function Find the constant a such that the function   is continuous on the entire real line. is continuous on the entire real line.

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Find the constant a such that the function Find the constant a such that the function   is continuous on the entire real line. is continuous on the entire real line.

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Find the limit (if it exists). Note that Find the limit (if it exists). Note that   represents the greatest integer function.  represents the greatest integer function. Find the limit (if it exists). Note that   represents the greatest integer function.

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Find the limit (if it exists). Find the limit (if it exists).

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Use the graph to determine the following limits, and discuss the continuity of the function at Use the graph to determine the following limits, and discuss the continuity of the function at   . (i)   (ii)   (iii)    . (i) Use the graph to determine the following limits, and discuss the continuity of the function at   . (i)   (ii)   (iii)    (ii) Use the graph to determine the following limits, and discuss the continuity of the function at   . (i)   (ii)   (iii)    (iii) Use the graph to determine the following limits, and discuss the continuity of the function at   . (i)   (ii)   (iii)    Use the graph to determine the following limits, and discuss the continuity of the function at   . (i)   (ii)   (iii)

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Find the x-values (if any) at which the function Find the x-values (if any) at which the function   is not continuous. Which of the discontinuities are removable? is not continuous. Which of the discontinuities are removable?

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Find the x-values (if any) at which the function Find the x-values (if any) at which the function   is not continuous. Which of the discontinuities are removable? is not continuous. Which of the discontinuities are removable?

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Find the x-values (if any) at which Find the x-values (if any) at which   is not continuous. is not continuous.

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A long distance phone service charges $ A long distance phone service charges $   for the first   minutes and $   for each additional minute or fraction thereof. Use the greatest integer function to write the cost C of a call in terms of time t (in minutes). for the first A long distance phone service charges $   for the first   minutes and $   for each additional minute or fraction thereof. Use the greatest integer function to write the cost C of a call in terms of time t (in minutes). minutes and $ A long distance phone service charges $   for the first   minutes and $   for each additional minute or fraction thereof. Use the greatest integer function to write the cost C of a call in terms of time t (in minutes). for each additional minute or fraction thereof. Use the greatest integer function to write the cost C of a call in terms of time t (in minutes).

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Find the x-values (if any) at which the function Find the x-values (if any) at which the function   is not continuous. Which of the discontinuities are removable? is not continuous. Which of the discontinuities are removable?

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