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
Another one Joshua — let's solve it. To evaluate the limit _x 0^- (x-1)/(x^2(x+2)), we will analyze the behavior of the numerator and the denominator as x approaches 0 from the left side. Step 1: Evaluate the numerator as x 0^-. As x approaches 0 from the left, x-1 approaches 0-1. _x 0^- (x-1) = -1 Step 2: Evaluate the denominator as x 0^-. The denominator is x^2(x+2). As x approaches 0 from the left, x^2 will be a very small positive number (e.g., (-0.001)^2 = 0.000001). So, x^2 0^+. As x approaches 0 from the left, x+2 approaches 0+2. _x 0^- x^2 = 0^+ _x 0^- (x+2) = 2 Therefore, the denominator x^2(x+2) approaches (0^+)(2), which is 0^+. Step 3: Combine the results for the numerator and denominator. The limit becomes a negative number divided by a very small positive number. _x 0^- (x-1)/(x^2(x+2)) = (-1)/(0^+) Step 4: Determine the final value of the limit. When a negative number is divided by a very small positive number, the result tends to negative infinity. (-1)/(0^+) = - The final answer is -. Send me the next one 📸