This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the limit expression. The given limit is: _x 2 (x^2 - 4)/(x - 2) Step 2: Check for indeterminate form. If we substitute x=2 directly into the expression, we get (2^2 - 4)/(2 - 2) = (4 - 4)/(0) = (0)/(0), which is an indeterminate form. This means we need to simplify the expression. Step 3: Factor the numerator. The numerator x^2 - 4 is a difference of squares, which can be factored as (x - 2)(x + 2). x^2 - 4 = (x - 2)(x + 2) Step 4: Simplify the expression. Substitute the factored numerator back into the limit expression: _x 2 ((x - 2)(x + 2))/(x - 2) Since x 2, x is approaching 2 but is not equal to 2. Therefore, x - 2 ≠ 0, and we can cancel out the (x - 2) term from the numerator and denominator. _x 2 (x + 2) Step 5: Evaluate the limit. Now, substitute x=2 into the simplified expression: 2 + 2 = 4 The limit is 4. Send me the next one 📸