Evaluating Limits Algebraically AP Calculus Ms. Olifer Objective: You will use the properties of limits to evaluate limits algebraically. You will also evaluate limits involving infinity algebraically and conceptually.
Properties of Limits
Continuous Intervals Such functions are “well-behaved” functions on these intervals and their limits can be evaluated by direct substitution. *Note: All polynomial functions are “well-behaved” functions and therefore are continuous on the interval
Limits of a Constant Value: (think about the graph) Evaluate each limit: These are continuous functions, so the direction that we are approaching doesn’t necessarily matter.
Limits of Polynomial Functions
Example
Indeterminate Form We say that f(x) has an indeterminate form (or is indeterminate) at x = c if the formula for f(c) yields an undefined expression of the type
WHAT to DO??? STRATEGY: Transform f(x) algebraically, if possible, into a new expression that is defined and continuous at x = c, and then evaluate the limit by substitution.
Flowchart for Evaluating Limits Analytically
Example (continued)
Multiplying by the Conjugate
Evaluate:
Infinite But Not Indeterminate Evaluate: Substitution leads to f(x) is not indeterminate at x = 2 Graph on pg. 93 Limit doesn’t exist
See yu tmrrw!