Question

Find the limit of the function algebraically.
lim as x approaches -2 (x^2 - 4) / (x + 2)

Answer 1

The limit of the function (x^2 - 4) / (x + 2) as x approaches -2 is found by factoring the numerator and simplifying the expression. After canceling out like terms, the limit is determined to be -4.

Step-by-step explanation:

The student has asked to find the limit algebraically of the function as x approaches -2 for the expression (x2 - 4) / (x + 2). To solve this, one can factor the numerator and then simplify the expression.

Firstly, factor the numerator which is a difference of squares:

• x2 - 4 = (x + 2)(x - 2)

Now, plug this into the original expression and simplify:

• (x2 - 4) / (x + 2) = ((x + 2)(x - 2)) / (x + 2)

Since x is approaching -2, but is not exactly -2, we can cancel out the (x + 2) terms:

• ((x + 2)(x - 2)) / (x + 2) = x - 2

The expression now is x - 2, and taking the limit as x approaches -2:

• lim as x -> -2 of (x - 2) = -2 - 2 = -4

Therefore, the limit of the function as x approaches -2 is -4.