Find the slowest growing and the fastest growing functions as x→∞ .
-$\begin{array} { l }
y = x + 7 \
y = e ^ { x } \
y = x ^ { 3 } + \cos ^ { 2 } x \
y = 4 ^ { x }
\end{array}$
A) Slowest: $y = x + 7$
Fastest: $\mathrm { y } = \mathrm { e } ^ { \mathrm { X } }$

B) Slowest: $y = e ^ { x }$
Fastest: $y = x ^ { 3 } + \cos ^ { 2 } x$

C) Slowest: $y = x + 7$
Fastest: $y = x ^ { 3 } + \cos ^ { 2 } x$

D) Slowest: $y = x + 7$
Fastest: $y = 4 ^ { x }$

Question

Find the slowest growing and the fastest growing functions as x→∞ .
-$\begin{array} { l } 
y = x + 7 \
y = e ^ { x } \
y = x ^ { 3 } + \cos ^ { 2 } x \
y = 4 ^ { x }
\end{array}$
A) Slowest: $y = x + 7$
Fastest: $\mathrm { y } = \mathrm { e } ^ { \mathrm { X } }$

B) Slowest: $y = e ^ { x }$
Fastest: $y = x ^ { 3 } + \cos ^ { 2 } x$

C) Slowest: $y = x + 7$
Fastest: $y = x ^ { 3 } + \cos ^ { 2 } x$

D) Slowest: $y = x + 7$
Fastest: $y = 4 ^ { x }$

Quizplus · Accepted Answer

The slowest growing function is $y = x + 7$ because it is linear, and among the given options, linear growth is slower than polynomial (cubic in this case) and exponential growth. The fastest growing function is $y = 4^x$ because exponential functions grow faster than both linear and polynomial functions, and $4^x$ grows faster than $e^x$ for large values of $x$.

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