The limits involving trig functions have two cases according to the dummy variation: near 0 or near ∞. The answers and the techniques used in these two cases have almost nothing in common. But it’s important to note that we can’t tell what case we’re dealing with just by looking at...
Practice finding the limits of trig functions with these study tools. Answer quiz questions with an interactive quiz that is available to you at...
lim 2 6 x x x + − + + 3 2 1 = lim 2( 3) x x x + − + + = − -8 -6 -4 -2 2 -20 20 40 Limit and Trig Functions From the graph of trigs functions ( ) sin and ( ) cos f x x g x x = = we conclude that they are continuous everywhere -10 -5 5 10...
This was Weierstrass's point when he came up with his wacky non-differential, but continuous everywhere function. If you come up with some wacky function, it's not going to be clear that our intuition applies to it. And wacky functions come up in math, so you have to deal with them....
5 Examples: 3 lim 2 x x x 4 lim 2 3 lim x x 6 Properties of Limits Algebraic Properties Algebraic Properties of Limits: Let b and c be real numbers, let n be a positive integer, and let f and g be functions with the following properties: Too many to fit on this page…. 7 Pr...