Find the slowest growing and the fastest growing functions as x→∞ .
-$$\begin{array} { l }
y = x ^ { 2 } + 7 x \
y = x ^ { 2 } \
y = \sqrt { x ^ { 4 } + x ^ { 2 } } \
y = 2 x ^ { 2 }
\end{array}$$
A) Slowest: $y = \sqrt { x ^ { 4 } + x ^ { 2 } }$
Fastest: $y = 2 x ^ { 2 }$
B) Slowest: $y = x ^ { 2 }$ and $y = 2 x ^ { 2 }$ grow at the same rate.
Fastest: $y = \sqrt { x ^ { 4 } + x ^ { 2 } }$
C) Slowest: $y = \sqrt { x ^ { 4 } + x ^ { 2 } }$
Fastest: $y = x ^ { 2 } + 7 x$
D) They all grow at the same rate.

Question

Find the slowest growing and the fastest growing functions as x→∞ .
-$$\begin{array} { l } 
y = x ^ { 2 } + 7 x \
y = x ^ { 2 } \
y = \sqrt { x ^ { 4 } + x ^ { 2 } } \
y = 2 x ^ { 2 }
\end{array}$$
A) Slowest: $y = \sqrt { x ^ { 4 } + x ^ { 2 } }$
Fastest: $y = 2 x ^ { 2 }$
B) Slowest: $y = x ^ { 2 }$ and $y = 2 x ^ { 2 }$ grow at the same rate.
Fastest: $y = \sqrt { x ^ { 4 } + x ^ { 2 } }$
C) Slowest: $y = \sqrt { x ^ { 4 } + x ^ { 2 } }$
Fastest: $y = x ^ { 2 } + 7 x$
D) They all grow at the same rate.

Quizplus · Accepted Answer

All functions are asymptotically equivalent to $y = x^2$ as $x \to \infty$, so they all grow at the same rate.

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