Evaluate the Limit limit as x approaches 8 of (1-4/x)^x

Problem

(lim_x→∞)(1−4/x)

Solution

1. Identify the form of the limit as x approaches infinity.

2. Recognize that the expression (1−4/x)x matches the standard limit definition for the exponential constant e

3. Apply the formula (lim_n→∞)(1+a/n)=ea

4. Substitute a=−4 into the formula to find the result.

Final Answer

(lim_x→∞)(1−4/x)=e(−4)

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