Understanding Function Growth Rates

The video tutorial explains how to rank the growth rates of various functions. It introduces two methods: comparing functions using limits and referring to a growth ranking table. The tutorial demonstrates how to use the table to rank functions from fastest to slowest growth, providing examples and explanations for each step. The fastest growing function is identified as an exponential function, followed by quadratic, linear, and logarithmic functions, with constants being the slowest. The tutorial concludes with a summary of the rankings.

What is the primary goal when ranking the growth rates of functions?

• To rank functions based on their growth speed

• To identify the function with the largest initial value

• To find the function with the smallest constant factor

• To determine which function is the most complex

Which method involves using limits to compare the growth of two functions?

• Graphical analysis

• Substitution method

• Integration method

• Limit comparison

What does the result of the limit comparison indicate?

• The function with the larger initial value

• The function with the higher order of growth

• The function with the smaller constant factor

• The function with the lower order of growth

What is the purpose of the growth ranking table?

• To list functions in alphabetical order

• To compare functions based on their initial values

• To rank functions by increasing complexity

• To determine the smallest constant factor

How should the growth ranking table be read to list functions from fastest to slowest growing?

• From top to bottom

• From left to right

• From right to left

• From bottom to top

Which function form is identified as the fastest growing in the given example?

• n

• c to the power of n

• log n

• n squared

What is the next fastest growing function after c to the power of n?

• n squared

• log n

• n

• square root of n

Which function is ranked as the slowest growing?

• n squared

• square root of n

• log n

• constant function

What is the correct order of growth for the functions log n, n, and square root of n?

• n, log n, square root of n

• square root of n, log n, n

• n, square root of n, log n

• log n, n, square root of n

Which function is ranked just before the constant function in terms of growth rate?

• n

• square root of n

• log n

• n squared