4 ms·
Another good way to see the limit definition is by solving the discrete case of that diff. equation (y' = y, y(0)=1). Replace dy/dx with ∆y/∆x, so ∆y = y(x+∆x
by huachimingo 5y ago
Another good way to see the limit definition is by solving the discrete case of that diff. equation (y' = y, y(0)=1).
Replace dy/dx with ∆y/∆x, so
∆y = y(x+∆x) - y(x)
Once you solve that (use some induction and numerical methods), see what happens when ∆x appraches to 0 and x=1.
For example try with ∆x=1 and then generalize that case to ∆x=n.
- hota_mazi 5y agoYou didn't justify why you picked y' = y, though, and I'm having a hard time connecting that differential equation with the one that follows "so" in your message. Could you break it down further?