Section Summary: 4.4

  1. Definitions

  2. Theorems

  3. Properties/Tricks/Hints/Etc.

  4. Summary

    Section 4.4 provides us with intuitive and formal definitions of infinite limits (that is, as the independent variable x tends toward negative or positive tex2html_wrap_inline217 ). The notion of a horizontal asymptote is introduced, which is a horizontal line towards which the function tends. This allows us to effectively replace a function, which may be rather complicated, by a number when we get to extreme values of x.

    An example of this use of approximation is the force of gravity: it's usually given as 9.81 meters per second squared, and we don't generally ask our distance from the center of the Earth. Gravity falls off as you get farther from the surface of the Earth, toward zero, but this change is so gradual that we treat this force as a constant. If we got far enough away from the Earth, we might treat its force of gravity as another constant - i.e. 0! That is the limit of Earth's gravity as we get ``infinitely far'' away (as if we can!).

Problems:

Problems, pp. 260-263, #2, 3, 10, 16, 38, 42, 56

At seats/On the board: 3, 4, 12, 17, 27, 25, 37, 41





LONG ANDREW E
Thu Mar 1 11:33:50 EST 2001