Comparing Growth Rates at Infinity Worksheet with Answer Key

What's on the worksheet

1. Find each limit with the ladder, writing ∞ for a quotient that grows without bound.
   \displaystyle \lim_{x \to \infty} \dfrac{x^{3/2}}{(\ln x)^6}\displaystyle \lim_{x \to \infty} \dfrac{\ln(x^3)}{\sqrt[4]{x}}\displaystyle \lim_{x \to \infty} \dfrac{x^8\, 2^x}{3^x}\displaystyle \lim_{x \to \infty} \dfrac{\ln(x^5)}{\ln(x^2)}
2. Find the limit.
3. Rank these six functions from slowest growing to fastest.
4. Find each limit.
5. Layla tracks two videos she posted online.
6. Samir makes three claims.