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Calculus: Limits


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Let [math]f(x) = (1 + \frac{1}{x})^{x}[/math]


a. Find the domain of f.

b. Draw the graph of f.

c. Explain why x=-1 and x=0 are points of discontinuity of f.

d. Are either of the discontinuities in part c removable? Explain.

e. Use graphs and tables to estimate [math]\lim_{x\to\infty} f(x)[/math]


I don't really know how to do a. There are a lot of values between -1 and 0 that are undefined. B and C are easy enough. D I have trouble because I don't know how to find the limit with the exponent. Would substitution be valid? And e I can handle.


Thank you!

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