On Friday, we went over sections 2.5 and 2.6, which discussed limits involving the transcendental functions: trigonometric functions and exponential and logarithmic functions.

The good news was that all of these functions, as long as we stay away from any "bad" x-values, work with our "plug-in" method for limits. We learned about two special limits involving the sine and cosine functions as we approach x = 0. We also looked at the limits at plus and minus infinity for exponential functions, as well as the limit at infinity for logarithmic functions (assuming the base is greater than 1). Logarithmic functions have a vertical asymptote at x = 0, so they have a limit approaching 0 from the right.

We took a look at the most commonly used base for exponential and logarithmic functions, the natural base e.



We found that

,

a fact which we sort of learned back in the days when we looked at compound interest problems.

We'll talk about continuity on Monday.