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Example 1: Find the limit
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Solution
we will use :
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Example 2:
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Solution :
Direct substitution gives the indeterminate form 0/0. The numerator can be seperated into the product of the two binomials (x+5) and (x-2).
So the limit is equivalent to

From here, we can simply divide (x - 2) out of the fraction. We do not have to worry about (x - 2) being equal to 0, since in the context of this limit, the expression can be treated as if x will never equal 2.
This gives us
The expression inside the limit is
now linear, so the limit can be found by direct substitution. This obtains 2 +
5 = 7.
We then can say that
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Example3:
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Solution:
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Example 4:
Find the limit
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Solution:
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Example 5:
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