EVALUATING HORIZONTAL AND VERTICAL ASYMPTOTES LIMITS WORKSHEET

Evaluate each limit and then identify any horizontal asymptotes.

Problem 1 :

xx3+8x-42x3+3

Solution

Problem 2 :

xx2-12x3-8x2+3

Solution

Problem 3 :

xx5-x-16x3

Solution

Problem 4 :

xx+1x2-1

Solution

Problem 5 :

xx2-1x+1

Solution

Problem 6 :

x25x2+xx-2

Solution

Problem 7 :

x1x(x-1)3

Solution

Problem 8 :

x-3x2+2x-15x2-9

Solution

Answer Key

1)  equation of the horizontal asymptote is y = 1/2.

2)  equation of the horizontal asymptote is y = 0 which is the x-axis.

3)  there is no horizontal asymptote. Slant  asymptote  will be there.

4)   equation of the horizontal asymptote is y = 0 which is the x-axis.

5)  there is no horizontal asymptote.

6)  the equation of the vertical asymptote is x = 2.

7)  the equation of the vertical asymptote is x = 1.

8)  equation of the vertical asymptote is x = 3.

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