Expert: Paul Klarreich - 8/17/2007

Question
I'm attempting to learn Calculus l on my own, after being out of school 30 years and most of the material I read don't go into detail enough to help me undertsand.

Use the Squeeze Law of limits to find the limit. limx =>0 x2 sin210x

Answer
Hi, John,

Try this:

lim   x^2 sin^2(10x)
x->0

[I assume that is what you meant to write.]

For all x,  -1 <= sin(10x) <= 1

Multiply all three sides by  x^2 and therefore, for all x,

-x^2 <= x^2 sin(10x) <= x^2, because  x^2 is never negative, so we don't have any messy switching of inequalities.

Now  lim -x^2 = 0  and  lim x^2 = 0, and now you can apply your squeeze theorem.