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→Example 3
:::<math>\forall n< \infty\quad\lim_{x\rightarrow\infty} \frac{x^n}{e^x}=
:::<math>\forall n< \infty\quad\lim_{x\rightarrow\infty} \frac{x^n}{e^x}=
\lim_{x\rightarrow\infty} \frac{nx^{n-1}}{e^x}=
\lim_{x\rightarrow\infty} \frac{nx^{n-1}}{e^x}=
\lim_{x\rightarrow\infty} \frac{n\left(n-1\right)x^{n-2}}{e^x}= \cdots
\lim_{x\rightarrow\infty} \frac{n\left(n-1\right)x^{n-2}}{e^x}= \cdots=
\lim_{x\rightarrow\infty} \frac{\left[n \left(n-1 \right)\left(n-2 \right)\cdots \left(n-\lfloor n \rfloor \right) \right]x^{n-\lceil n \rceil}}{e^x}</math>
\lim_{x\rightarrow\infty} \frac{\left[n \left(n-1 \right)\left(n-2 \right)\cdots \left(n-\lfloor n \rfloor \right) \right]x^{n-\lceil n \rceil}}{e^x}</math>
:::(where <math>\lfloor n \rfloor</math> is the [[floor function]] of n and <math>\lceil n \rceil</math> is the [[ceiling function]] of n)
:::(where <math>\lfloor n \rfloor</math> is the [[floor function]] of n and <math>\lceil n \rceil</math> is the [[ceiling function]] of n)