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mathematics UK Year 12 Mathematics (AS)
 
Solved problems for the chapter:
 

Limits at Infinity and Vertical Asymptotes

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Limits at infinity
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:limits_at_infinity_and_vertical_asymptotes/4794/


Example 1.

Evaluate .

    
Example 2.

Evaluate:


    
3.

Calculate the following limit:


    
4.

Calculate the following limit:


    
5.

Calculate the following limit:


    
6.

Evaluate:


    
7.

Evaluate:


    
8.

Evaluate:


    

9.

Evaluate:


    
10.

Evaluate:


    
11.

Calculate the following limit:


    
12.

Evaluate:


    
13.

Obtain the equation of the horizontal asymptote of the function and draw its graph:


    
14.

Evaluate:


    
15.

Evaluate:


    
16.

Evaluate:


    
17.

Evaluate:


    
18.

Obtain the equation of the horizontal asymptote of the function and draw its graph:


    

19.

Obtain the equation of the horizontal asymptote of the function below and draw its graph:


    
20.

Obtain the equation of the horizontal asymptote of the function and draw its graph:


    
21.

Write the equation of the horizontal asymptote of the function and draw its graph:


    
22.

Obtain the equation of the horizontal asymptote of the function and draw its graph:


    
23.

A function is given as:




  • Obtain the equation of the oblique asymptote of the function.


  • Sketch the graph of the function.

    
24.

Obtain the equation of the oblique asymptote of the function below and draw its graph:


    
25.

Obtain the equation of the oblique asymptote of the function below and draw its graph:


    
26.

Obtain the equation of the oblique asymptote of the function below and draw its graph: