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
Here are the solutions for the limits: Problem 9: Step 1: Substitute x=-2 into the expression. _x -2 ((x)/(x + 1)) ((3x + 5)/(x^2 + x)) = ((-2)/(-2 + 1)) ((3(-2) + 5)/((-2)^2 + (-2))) Step 2: Simplify each fraction. ((-2)/(-1)) ((-6 + 5)/(4 - 2)) = (2) ((-1)/(2)) Step 3: Multiply the results. 2 × (-(1)/(2)) = -1 The limit is -1. Problem 10: Step 1: Substitute x=1 into the expression. _x 1 ((1)/(x + 1)) ((x + 6)/(x)) ((3 - x)/(7)) = ((1)/(1 + 1)) ((1 + 6)/(1)) ((3 - 1)/(7)) Step 2: Simplify each fraction. ((1)/(2)) ((7)/(1)) ((2)/(7)) Step 3: Multiply the results. (1)/(2) × 7 × (2)/(7) = 1 The limit is 1. Problem 11: Step 1: Factor the numerator x^2 - x - 2. x^2 - x - 2 = (x - 2)(x + 1) Step 2: Simplify the expression by canceling the common factor (x + 1). _x -1 ((x - 2)(x + 1))/(x + 1) = _x -1 (x - 2) Step 3: Substitute x=-1 into the simplified expression. -1 - 2 = -3 The limit is -3. Problem 12: Step 1: Factor the numerator x^2 - x - 2. x^2 - x - 2 = (x - 2)(x + 1) Step 2: ✂️ _That answer was long and got cut off. Reply continue and I'll finish it._