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

question 137

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: \(y = x e ^ { x }\)

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Definitions:

Locus of Control

A psychological concept that refers to how strongly people believe they have control over the situations and experiences that affect their lives.

Internal Locus

The belief that one controls their own life and outcomes, rather than external forces.

External Locus

The belief that one's life events are largely influenced by external forces or the environment rather than personal actions.

Toe Dipper

An individual or entity that cautiously tests or explores a new venture, idea, or market with minimal commitment.