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

question 6

Multiple Choice

Find the slowest growing and the fastest growing functions as x→∞ .
- $$\begin{array} { l } y = e ^ { x } \\y = e ^ { x / 7 } \\y = x ^ { x } \\y = 4 ^ { x }\end{array}$$

• A) Slowest: \(y = e ^ { x / 7 }\)
• Fastest: \(\mathrm { y } = \mathrm { x } ^ { \mathrm { x } }\)
• B) Slowest: \(\mathrm { y } = \mathrm { e } ^ { \mathrm { x } / 7 }\) and \(\mathrm { y } = \mathrm { e } ^ { \mathrm { x } }\) grow at the same rate.
• Fastest: \(y = 4 ^ { x }\)
• C) Slowest: \(y = x ^ { x }\)
• Fastest: \(y = 4 ^ { x }\)
• D) Slowest: \(y = e ^ { x / 7 }\) and \(y = e ^ { x }\) grow at the same rate.
• Fastest: \(\mathrm { y } = \mathrm { x } ^ { \mathrm { x } }\)

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