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

question 7

Multiple Choice

Find the slowest growing and the fastest growing functions as x→∞ .
- $$\begin{array} { l } y = \ln 2 x \\y = 5 \ln x \\y = \frac { 1 } { x } \\y = \sqrt { x }\end{array}$$

• A) Slowest: \(y = \frac { 1 } { x }\)
• Fastest: \(y = \sqrt { x }\)
• B) Slowest: \(y = \frac { 1 } { x }\)
• Fastest: \(y = 5 \ln x\)
• C) Slowest: \(y = \sqrt { x }\)
• Fastest: \(y = \ln 2 x\) and \(y = 5 \ln x\) grow at the same rate.
• D) Slowest: \(y = \ln 2 x\) and \(y = 5 \ln x\) grow at the same rate. Fastest: \(y = \sqrt { x }\)

---

Definitions:

March

The third month of the year in the Gregorian calendar, often associated with financial and performance reporting for the first quarter.

Labor Efficiency Variance

The difference between the actual hours worked and the standard hours expected to produce a certain level of output, valued at the standard labor rate.

February

The second month in the Gregorian calendar, recognized for its 28 days in regular years and 29 days during leap years.

Variable Overhead Efficiency Variance

The difference between the actual variable overhead based on hours worked and the standard cost of variable overhead for the actual hours worked.