Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.5 Exercises - Page 364: 104

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For x = 1, $(1+x)^{1/x} = (1+1)^1 =2$ For x = 0.1, $(1+x)^{1/x} = (1.1)^{1/0.1} = 1.1^{10}=2.6$ For x = 0.01, $(1+x)^{1/x} = (1.01)^{100} =2.704$ For x = 0.0001, $(1+x)^{1/x} = (1.0001)^{1000} =2.71815$ For x = 0.000001, $(1+x)^{1/x} = (1.000001)^{1000000} =2.71828$ We see that for smaller and smaller values of x, the value of the function approaches the value of $e$.