To evaluate: The limit of the function .
The limit of the function is .
Suppose that c is a constant and the limits and exist, then
Limit law 2:
Limit law 7:
Limit law 8:
Direct substitution property:
If f is a polynomial or a rational function and a is in the domain of f, then .
If when , then , provided the limit exist.
Compute the limit value of the denominator.
Since the limit of the denominator is zero, the quotient law cannot be applied.
Simplify by using elementary algebra.
Factorize the numerator ,
Substitute for in equation (1).
Take the common terms out from the numerator, .
Cancel the common terms from both the numerator and the denominator, .
Use fact 1, and , then .
Apply direct substitution property on the limit function.
Thus, the limit of the function is .
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