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: Simplify the denominator of the expression. The denominator is (x-1) ÷ (x-1). Since x 1^-, x is approaching 1 but is not equal to 1. Therefore, x-1 ≠ 0. For any a ≠ 0, a ÷ a = 1. So, (x-1) ÷ (x-1) = 1. The limit expression simplifies to: _x 1^- (e^1)/(x-1)1 = _x 1^- e^(1)/(x-1) Step 2: Evaluate the argument of the exponential function. Let u = (1)/(x-1). As x approaches 1 from the left side (x 1^-), the term x-1 approaches 0 from the negative side (x-1 0^-). Therefore, u = (1)/(x-1) approaches (1)/(0^-), which is -. Step 3: Substitute the new limit variable into the expression. The limit becomes: _u - e^u Step 4: Evaluate the limit. As u approaches -, the value of e^u approaches 0. _u - e^u = 0 The final answer is 0. That's 2 down. 3 left today — send the next one.