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
Let's find the limit of the given function. The problem asks to evaluate the limit: _x (1 - (2)/(x))^x Step 1: Recognize the form of the limit. This limit is in the indeterminate form 1^ as x , since (1 - (2)/(x)) (1 - 0) = 1. This form is related to the definition of the mathematical constant e. Step 2: Apply the standard limit formula for e. A common limit definition for e is: _x (1 + (k)/(x))^x = e^k where k is a constant. Step 3: Compare the given limit with the standard formula. In our problem, we have (1 - (2)/(x))^x. We can rewrite this as (1 + (-2)/(x))^x. By comparing this to the standard formula, we can identify k = -2. Step 4: Substitute the value of k into the formula. Using k = -2: _x (1 + (-2)/(x))^x = e^-2 Step 5: Express the result with a positive exponent. e^-2 = (1)/(e^2) The final answer is: (1)/(e^2) Send me the next one 📸