Advanced Math/analysis ?

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Expert: Sherry Wallin - 11/18/2008


Question
Prove that if f(x) = e^x, then
(a) f(x) is strictly increasing for all x in R;
(b) lim as x goes to +infinity f(x) = 1;
(c) lim as x goes to -infinity f(x) = 0

Answer
Take the derivative of e^x and it is of course e^x > 0 for all x so e^x is strictly increasing. lim x-> infinity is NOT 1, it is infinity. Using part a this is obvious since it is a strictly increasing for all x in R, so it can't be 1. lim x-> -infinity is 1/e^x and 1/ any number to a high power is 1/ huge number which is a big fat 0.

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Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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