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
You're asking about the third limit problem: _x (2 + 5x + x x)/(x^2 - 3x). When we divide the entire numerator by x^2, we divide each term in the numerator separately: (2 + 5x + x x)/(x^2) = (2)/(x^2) + (5x)/(x^2) + (x x)/(x^2) This simplifies to: (2)/(x^2) + (5)/(x) + ( x)/(x) As x : (2)/(x^2) 0 (5)/(x) 0 ( x)/(x) 0 (due to the Squeeze Theorem, as -1 x 1) So, the entire numerator approaches 0 + 0 + 0 = 0. The term (3)/(x) actually appears in the denominator after dividing by x^2: (x^2 - 3x)/(x^2) = (x^2)/(x^2) - (3x)/(x^2) = 1 - (3)/(x) As x , this denominator approaches 1 - 0 = 1. Therefore, the limit is (0)/(1) = 0. Drop the next question.