Question

How do you find the limit of `(sqrt(1+h)-1)/h` as h approaches 0?

Answer 1

I found: `1/2`

Explanation:

If you try the limit directly you'll get the indeterminate form `0/0`;
To avoid this I 'd try a little manipulation, a kind of "strange" inverse rationalization (orange circle). Have a look:

Graphically
graph{(sqrt(1+x)-1)/x [-10, 10, -5, 5]}