Find the Slowest Growing and the Fastest Growing Functions as X→∞

Multiple Choice

Find the slowest growing and the fastest growing functions as x→∞ .
- $$\begin{array} { l } y = 7 x ^ { 10 } \\y = e ^ { x } \\y = e ^ { x - 2 } \\y = x e ^ { x }\end{array}$$

A) Slowest: $y = 7 x ^ { 10 }$
Fastest: $y = e ^ { x }$ and $y = e ^ { x - 2 }$ grow at the same rate.
B) Slowest: $y = x e ^ { x }$
Fastest: $\mathrm { y } = \mathrm { e } ^ { \mathrm { x } }$
C) Slowest: $y = e ^ { x - 2 }$
Fastest: $y = x e ^ { x }$
D) Slowest: $\mathrm { y } = 7 \mathrm { x } ^ { 10 }$
Fastest: $y = x e ^ { x }$