Multiplicity of root
Posted: Mon Jan 11, 2016 1:54 pm
Given the function $f(x)=e^x-x-1$ prove that $0$ is a zero of $f$ of multiplicity $2$.
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It suffices to prove that the limit $\displaystyle \lim \limits_{x \rightarrow 0} \frac{f(x)}{x^2}$ is finite. However,Tolaso J Kos wrote:Given the function $f(x)=e^x-x-1$ prove that $0$ is a zero of $f$ of multiplicity $2$.