FORMULAS IN EVALUATING LIMITS

Evaluate the indicated limit :

Example 1 :

Solution :

Example 2 :

Solution :

Example 3 :

Solution :

Example 4 :

Solution :

Let y = 5x.

When x = 0,

y = 5(0)

y = 0

When x ---> 0, y ---> 0.

Example 5 :

Solution :

Let y = 3x.

When x = 0,

y = 3(0)

y = 0

When x ---> 0, y ---> 0.

Example 6 :

Solution :

Example 7 :

Solution :

Example 8 :

Solution :

Example 9 :

Solution :

Let y = ˣ⁄₃.

When x ---> ,

y ---> ⁄₃

y ---> 

Note :

From the above problem, we can derive the following result.

Example 10 :

where k and m are constants.

Solution :

By direct substitution,

Example 11 :

Solution :

Let y = 2x2.

When x ---> , y ---> .

Example 12 :

Solution :

Let y = 2x2.

When x ---> x ---> .

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