Find the limit: lim (x -> 2) (x^2 - 4)/(x - 2)

₹0.0

Question: Find the limit: lim (x -> 2) (x^2 - 4)/(x - 2)

Options:

Correct Answer: 4

Solution:

The expression (x^2 - 4)/(x - 2) can be factored as (x - 2)(x + 2)/(x - 2). Canceling (x - 2) gives lim (x -> 2) (x + 2) = 4.

Find the limit: lim (x -> 2) (x^2 - 4)/(x - 2)

Find the limit: lim (x -> 2) (x^2 - 4)/(x - 2)

Step 1: Identify the limit we want to find: lim (x -> 2) (x^2 - 4)/(x - 2).
Step 2: Notice that the expression (x^2 - 4) can be rewritten using the difference of squares: (x^2 - 4) = (x - 2)(x + 2).
Step 3: Substitute this factorization into the limit: lim (x -> 2) ((x - 2)(x + 2))/(x - 2).
Step 4: Since (x - 2) is in both the numerator and the denominator, we can cancel it out, but only for x ≠ 2: lim (x -> 2) (x + 2).
Step 5: Now, we can directly substitute x = 2 into the simplified expression: (2 + 2) = 4.
Step 6: Therefore, the limit is 4.

Limit Evaluation – Understanding how to evaluate limits, especially when dealing with indeterminate forms.
Factoring and Simplification – The ability to factor expressions and simplify them to resolve limits.