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The screen shows a table of selected values for the function defined by $Y_{1}=\left(1+\frac{1}{X}\right)^{X}$(a) Why is there an error message for $X=0 ?$(b) What number does the function value seem to approach as $X$ takes on larger and larger values?(c) Use a calculator to evaluate this function for $\mathrm{X}=1,000,000 .$ What value do you get? Now evaluate $e=e^{1} .$ How close are these two values?(d) Make a conjecture: As the values of $x$ approach infinity, the value of $\left(1+\frac{1}{x}\right)^{x}$ approaches
Algebra
Chapter 12
Inverse, Exponential, and Logarithmic Functions
Section 6
Exponential and Logarithmic Equations; Further Applications
Functions
Exponential and Logarithmic Functions
Missouri State University
Oregon State University
Baylor University
Lectures
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Okay, so for port A. Well, we can't have XP quiches a role because we have division by fellow. Now for Part B. What values there's a function seem to approach as X takes on larger and larger volumes. What thing? It seems to take on the Value E, which is approximately 2.718 to 8.
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