HSF.LE.A.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Also written as F-LE.3 or F.LE.3

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Example Problems

Determine

\lim_{n \to \infty} \frac{n!}{n^n}

Find

\lim_{x \to \infty} \frac{e^{x}}{x^{10}}

.

Find

\lim_{x \to \infty} \frac{x^3 - x}{e^{x}}

.

Khan Academy Resources

Exponential vs. linear growth over time Exponential vs. linear growth over time Comparing growth of exponential & quadratic models

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