How Do You Simplify the Equation Involving Exponential Terms and Limits?

[BoT]

1. ex*eh+e-x*e-h -ex -e-x/ 2h




2. This should simplify to (e^x-e^-x)/2. This is lim (h--->0) so in the end the h should become 0 (I think!)



3. I have absolutely no idea what to do!

 

[sylas]

1. ex*eh+e-x*e-h -ex -e-x/ 2h




2. This should simplify to (e^x-e^-x)/2. This is lim (h--->0) so in the end the h should become 0 (I think!)



3. I have absolutely no idea what to do!

I presume your original equation is

\frac{e^x e^h + e^{-x} e^{-h} - e^x - e^{-x}}{2h}​

Look for some common factors.