Limit questions

Question

Evaluate the limit..

Lim _z-->∞    ln ( 1+e^z)/z

 

Answer 1

For very large z ln(1+exp(z)) can be replaced by ln(exp(z)) = z, and lim z/z =1 for z→∞.

Thus

                    lim _z→∞. ln(1+exp(z))/z = 1.

Keep in mind: exp(z) when z→∞, is a very rapidly growing function, and 1 is a negligibly small number compared with the exponent.