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

Derivatives and gradient functions

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Limits at infinity
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Infinite limits
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Derivatives of other elementary functions
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Limit of a function
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:derivatives_and_gradient_functions/5419/


Example 1.

Find the derivative of the function:


    
Example 2.

Calculate the derivative of the function:


    
3.

Find the derivative of the function:


.

    
4.

Calculate the limit:


    
5.

Evaluate .

    
6.

Calculate the following limit:


    
7.

For what real number a will the function:




have ?

    
8.

Find the derivative of the function:


.

    

9.

Calculate the limit:


    
10.

Evaluate:


    
11.

The function:




is given. Calculate the value of .

    
12.

Calculate the limit:


    
13.

Calculate the following limit:


    
14.

Write down the rise and fall intervals of the function


    
15.

Calculate the limit:


    
16.

Calculate the following limit:


    
17.

Find the derivative of the function:


    
18.

Calculate the limit:


    

19.

Calculate the following limit:


    
20.

Calculate the limit:


    
21.

Evaluate:


    
22.

Find the derivative of the function:


    
23.

Calculate the limit:


    
24.

Evaluate:


    
25.

Calculate the limit:


    
26.

Evaluate:


    
27.

Find the derivative of the function:


    
28.

Calculate the limit:


    

29.

Evaluate:


    
30.

Calculate the limit:


    
31.

Evaluate:


    
32.

Calculate the limit:


    
33.

Calculate the following limit:


    
34.

Calculate the limit:


    
35.

Evaluate:


    
36.

Calculate the limit:


    
37.

Find the derivative of the function:


.

    
38.

Calculate the limit:


    

39.

Evaluate:


    
40.

Calculate the derivative of the function:


.

    
41.

Calculate the limit:


    
42.

Evaluate:


    
43.

Calculate the derivative of the function:


.

    
44.

Calculate the limit:


    
45.

Evaluate:


    
46.

Find the derivative of the function:


    
47.

Calculate the limit:


    
48.

Evaluate:


    

49.

Calculate the limit:


    
50.

Calculate the limit:


    
51.

Calculate the limit:


    
52.

Calculate the limit:


    
53.

Find the derivative of the function:


    
54.

Calculate the limits:








    
55.

Calculate the following limit:


    
56.

Find the derivative of the function: