question 6 of 10 the value of which of these expressions is closest to e? a. (1 + 1/11)^11 b. (1 + 1/12)^12…

question 6 of 10 the value of which of these expressions is closest to e? a. (1 + 1/11)^11 b. (1 + 1/12)^12 c. (1 + 1/13)^13 d. (1 + 1/14)^14

question 6 of 10 the value of which of these expressions is closest to e? a. (1 + 1/11)^11 b. (1 + 1/12)^12 c. (1 + 1/13)^13 d. (1 + 1/14)^14

Answer

Explanation:

Step1: Recall the limit definition of e

The number (e) is defined as (\lim_{n\rightarrow\infty}(1 + \frac{1}{n})^n). The larger the value of (n), the closer the expression ((1+\frac{1}{n})^n) is to (e).

Step2: Compare the values of (n) in each option

In option A, (n = 11); in option B, (n=12); in option C, (n = 13); in option D, (n=14). Since (14>13>12>11), the expression ((1+\frac{1}{14})^{14}) is the closest to (e) among the given options.

Answer:

D. ((1+\frac{1}{14})^{14})