** 27.T Limits at infinity, infinite limits, asymptotes; Improper
integrals **

** Reference: ** Stewart 3.5, 1.2, 1.4, 7.9

** Keywords: ** Limit at infinity, infinite limit,
horizontal asymptote, vertical asymptote, improper integral, unbounded
function

** Learning Objectives: ** The student will be able to:

- State or recognize the precise definition of a limit at infinity and the precise definition of a limit whose value is infinity
- Use these definitions to prove limit statements in simple cases
- Relate limits involving infinity to horizontal and vertical asymptotes
- Evaluate improper integrals: integrals over infinite intervals, and integrals with unbounded integrand
- Use the "p-test" to determine whether improper integrals converge

** 27.R EXAM 6 **