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

question 101

Multiple Choice

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: \(y = 4 ^ { x }\)

---

Definitions:

Fixed Manufacturing Costs

Overhead expenses that do not vary with production level, such as rent, salaries, and utility costs in a manufacturing environment.

Margin of Safety

Margin of Safety is the difference between actual sales and the break-even point, indicating the amount of sales decline a company can sustain before incurring a loss.

CVP Income Statement

An income statement format that is used to analyze the impact of varying levels of sales and product costs on operating profit, focusing on the relationships between cost, volume, and profit.

Management Decision-Making

The process by which management identifies, evaluates, and chooses among alternative courses of action to achieve organizational objectives.