Final answer:
The limit of the function
as x approaches 2 is 4.
Explanation:
To evaluate limits, we need to determine the behavior of a function as it approaches a particular value. Let's consider an example to understand this concept better:
To evaluate this limit, we can directly substitute the value of x into the function. However, when x approaches the value of 2, we encounter a problem because the denominator becomes zero, which leads to an undefined expression.
To overcome this issue, we can simplify the expression by factoring the numerator: f(x) = ((x - 2)(x + 2)) / (x - 2).
Now, we can cancel out the common factor of (x - 2) in the numerator and denominator: f(x) = x + 2.
After simplifying, we have a new function f(x) = x + 2, which is defined for all real numbers.
Since the function f(x) = x + 2 is defined at x = 2, we can substitute the value of x and find the limit:
lim (x- > 2) f(x) = lim (x- > 2) (x + 2) = 4.
Therefore, the limit of the function
as x approaches 2 is 4.
In summary, when evaluating limits, we need to examine the behavior of the function as it approaches a specific value. In this example, we simplified the expression and canceled out the common factor to find the limit.
Your question is incomplete, but most probably the full question was:
lab 2 supplement evalute the following limits. show the steps
as x approaches 2.