Subject: Fwd: convergence
Hi, I am a high school senior and I need help stugying for a final. I am
stuck on one of the questions on my review sheet. Does the improper
integral from 5 to infinity of (38/97)^{x} converge or diverge? If it
converges I also need to know how to find the approximate value accurate to
.01 of its actual value. In your calculus class you have probably spent quite a bit of time on THE exponential function e^{x} and not much time on other exponential functions like 7^{x} or (38/97)^{x}. The reason is that any exponential function a^{x} can be written with base e as follows: Suppose that y = a^{x} then ln(y) = ln(a^{x}) = x ln(a) and hence y = e^{ln(y)} = e^{x ln(a)}. In your problem (38/97)^{x} = e^{x ln(38/79)} and hence find recalling that ln(38/79) = ln(38)  ln(79). Cheers,Harley
