12.4 Limits at Infinity/Sequences

12.4 Limits at Infinity and Limits of Sequences

The limit as x approaches infinity is just talking about end behavior

Step 1: plug in massive number into your equation

Step 2: get answer

Step 3: that answer is the limit at infinity

In sequences An is the same as f(x) 

When in doubt one can always plug numbers in

That wouldn't work if one would get 0/0 because that means indeterminate

12.3 The Tangent Line Problem

Slope 

The slope m of the graph f at the point (x,f(x)) is equal to the slope of its tangent line at (x,f(x)), and is given by:

which is equal to the difference quotient

Finding Slope of a Graph

Derivatives

The derivative of f at x is 

provided this limit exists