Exam 2: Section 5 : Limits and Their Properties

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Find the vertical asymptotes (if any) of the function Find the vertical asymptotes (if any) of the function   . .

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A petrol car is parked A petrol car is parked   feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of   revolution per second. The rate at which the light beam moves along the wall is   . Find the limit of r as   .  feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of A petrol car is parked   feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of   revolution per second. The rate at which the light beam moves along the wall is   . Find the limit of r as   .  revolution per second. The rate at which the light beam moves along the wall is A petrol car is parked   feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of   revolution per second. The rate at which the light beam moves along the wall is   . Find the limit of r as   .  . Find the limit of r as A petrol car is parked   feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of   revolution per second. The rate at which the light beam moves along the wall is   . Find the limit of r as   .  . A petrol car is parked   feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of   revolution per second. The rate at which the light beam moves along the wall is   . Find the limit of r as   .

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A petrol car is parked A petrol car is parked   feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of   revolution per second. The rate at which the light beam moves along the wall is   . Find the rate   when   is   .  feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of A petrol car is parked   feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of   revolution per second. The rate at which the light beam moves along the wall is   . Find the rate   when   is   .  revolution per second. The rate at which the light beam moves along the wall is A petrol car is parked   feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of   revolution per second. The rate at which the light beam moves along the wall is   . Find the rate   when   is   .  . Find the rate A petrol car is parked   feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of   revolution per second. The rate at which the light beam moves along the wall is   . Find the rate   when   is   .  when A petrol car is parked   feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of   revolution per second. The rate at which the light beam moves along the wall is   . Find the rate   when   is   .  is A petrol car is parked   feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of   revolution per second. The rate at which the light beam moves along the wall is   . Find the rate   when   is   .  . A petrol car is parked   feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of   revolution per second. The rate at which the light beam moves along the wall is   . Find the rate   when   is   .

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Find all the vertical asymptotes (if any) of the graph of the function Find all the vertical asymptotes (if any) of the graph of the function     . Find all the vertical asymptotes (if any) of the graph of the function     . .

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Determine whether Determine whether   approaches   or   as x approaches   from the left and from the right by completing the tables below.     -3.1 -3.01 -3)001     -2.999 -2)99 -2)9 -2)5  approaches Determine whether   approaches   or   as x approaches   from the left and from the right by completing the tables below.     -3.1 -3.01 -3)001     -2.999 -2)99 -2)9 -2)5  or Determine whether   approaches   or   as x approaches   from the left and from the right by completing the tables below.     -3.1 -3.01 -3)001     -2.999 -2)99 -2)9 -2)5  as x approaches Determine whether   approaches   or   as x approaches   from the left and from the right by completing the tables below.     -3.1 -3.01 -3)001     -2.999 -2)99 -2)9 -2)5  from the left and from the right by completing the tables below. Determine whether   approaches   or   as x approaches   from the left and from the right by completing the tables below.     -3.1 -3.01 -3)001     -2.999 -2)99 -2)9 -2)5  Determine whether   approaches   or   as x approaches   from the left and from the right by completing the tables below.     -3.1 -3.01 -3)001     -2.999 -2)99 -2)9 -2)5  -3.1 -3.01 -3)001 Determine whether   approaches   or   as x approaches   from the left and from the right by completing the tables below.     -3.1 -3.01 -3)001     -2.999 -2)99 -2)9 -2)5  Determine whether   approaches   or   as x approaches   from the left and from the right by completing the tables below.     -3.1 -3.01 -3)001     -2.999 -2)99 -2)9 -2)5  -2.999 -2)99 -2)9 -2)5 Determine whether   approaches   or   as x approaches   from the left and from the right by completing the tables below.     -3.1 -3.01 -3)001     -2.999 -2)99 -2)9 -2)5

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Find all the vertical asymptotes (if any) of the graph of the function Find all the vertical asymptotes (if any) of the graph of the function   . .

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

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Find all vertical asymptotes (if any) of the function Find all vertical asymptotes (if any) of the function   . .

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Use a graphing utility to graph the function Use a graphing utility to graph the function   and determine the following one-sided limit.  and determine the following one-sided limit. Use a graphing utility to graph the function   and determine the following one-sided limit.

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Find the vertical asymptotes (if any) of the function Find the vertical asymptotes (if any) of the function   . .

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Find all the vertical asymptotes (if any) of the graph of the function Find all the vertical asymptotes (if any) of the graph of the function

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Find the limit. Find the limit.

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A A   -foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of   , where x is the distance between the base of the ladder and the house. Find the rate r when x is   feet.  -foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of A   -foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of   , where x is the distance between the base of the ladder and the house. Find the rate r when x is   feet.  , where x is the distance between the base of the ladder and the house. Find the rate r when x is A   -foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of   , where x is the distance between the base of the ladder and the house. Find the rate r when x is   feet.  feet. A   -foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of   , where x is the distance between the base of the ladder and the house. Find the rate r when x is   feet.

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A 25-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of A 25-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of   where x is the distance between the base of the ladder and the house. Find the limit of r as   .  where x is the distance between the base of the ladder and the house. Find the limit of r as A 25-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of   where x is the distance between the base of the ladder and the house. Find the limit of r as   .  . A 25-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of   where x is the distance between the base of the ladder and the house. Find the limit of r as   .

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Use a graphing utility to graph the function Use a graphing utility to graph the function   and determine the one-sided limit   . and determine the one-sided limit Use a graphing utility to graph the function   and determine the one-sided limit   . .

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Find the limit. Find the limit.

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Find the following limit if it exists: Find the following limit if it exists:   . Use   when appropriate. . Use Find the following limit if it exists:   . Use   when appropriate. when appropriate.

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Find the limit. Find the limit.

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