RES.18-005 | Spring 2010 | Undergraduate

Highlights of Calculus

Derivatives (12 videos)

Growth Rate and Log Graphs

It is good to know how fast different functions grow.  Professor Strang puts them in order from slow to fast:
    logarithm of x    powers of x    exponential of x     x factorial    x to the x power   What is even faster??

And it is good to know how graphs can show the key numbers in the growth rate of a function
A LOG-LOG graph plots log y against log x   If y = A x^n then log y = log A + n log x == LINE WITH SLOPE n

A SEMILOG graph plots log y against x        If y = A 10^cx then log y = log A + cx == LINE WITH SLOPE c
You will never see y = 0 on these graphs because log 0 is minus infinity.  But n and c jump out clearly.

Professor Strang’s Calculus textbook (1st edition, 1991) is freely available here.

Subtitles are provided through the generous assistance of Jimmy Ren.

Course Info

As Taught In
Spring 2010