Evaluate the Limit limit as n approaches 8 of (1+1/n)^n

Problem

(lim_n→8)(1+1/n)

Solution

1. Identify the type of limit being evaluated. Since n is approaching a finite value 8 and the function is continuous at that point, we can use direct substitution.

2. Substitute the value n=8 into the expression.

(1+1/8)8

3. Simplify the expression inside the parentheses by finding a common denominator.

1+1/8=8/8+1/8=9/8

4. Evaluate the power by raising the fraction to the exponent of 8

(9/8)8

5. Calculate the numerical values for the numerator and denominator.

9=43046721

8=16777216

Final Answer

(lim_n→8)(1+1/n)=43046721/16777216

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