|« Properties of Limits|
Example 1: Find the limit
we will use :
Direct substitution gives the indeterminate form 0/0. The numerator can be separated 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
Find the limit