Visualization of limits
Introduction and Activity
Do you know the limits above? The purpose of the applet is to
visualize those limits.
First, let's choose two functions y=x and y=sin x. Then, scale up
the graph around the origin. You will see the two graphs are almost
same when you scale up enough. In other words, sin x and x have
almost same value when x is very small. This means sin x/x ->1 (x->0).
- Compare y=e^x-1 and y=x.
- Compare y=log(1+x) and y=x
Applet
- Compare the two graphs; y=1-cos x and y=x^2.
- Prove the formula abobe using lim sin x/x (x->0)=1.