2.6-2.9 Theory

To find the asymptotic behavior of a rational function, what do you do?

• Factor out the denominator’s largest variable from the top and bottom.

What are the conditions for the squeeze theorem?

• Suppose f(x) <= h(x) <= g(x), and suppose that the limit of f(x) and g(x) are both equal to L as they approach point c.

• Then, the limit of h(x) must also equal L.

List the two important trigonometric limits.

NOTE: cos(t)/t is NOT one of the limit identities.

List Theorem 3.

No, because the two limits between which f(x) is sandwiched are not the same.

Explain how to solve this.

• Upon applying the given identity, factor out a sin(x) and then go from there.

[T/F]: Horizontal asymptotes can include infinity/negative infinity.

False

Extra

Extra

Give an example where the limit of two functions’ sum exists, but the functions’ limits do not individually exist.

1/x and -1/x