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Without using differentiation, logarithmic function, rigorously, prove that $$e^x\ge x+1$$ for all real values of $x$.

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    Please avoid using display math (double \$\$) in titles.2012-12-06
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    Are you alowed to use MVT?2012-12-06
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    How do you define $e$ and/or $e^x$? What kind of answer is expected depends on the definition you are using.2012-12-06
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    Yes,I can use MVT, I want to prove it using only lim(1+x/n)n as n goest to inf2012-12-06
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    For positive x's I am done,but negative,I need help, have been trying it for hours...2012-12-06
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    Try using Bernoulli's inequality, see here http://en.wikipedia.org/wiki/Bernoulli%27s_inequality#Proof_For_Rational_Case2012-12-06
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    This is wrongly marked as duplicate since it from Dec 2012 and the other post is from 20132017-11-10

8 Answers 8