Finding Limits Analytically | Rice University

University
Rice University
Course
Preparing for the AP Calculus AB Exam
Pages

1

Academic year

2022
Author

Awayne
Views

83

p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:16px;font-family:ArialMT;color:#000000;} .ft02{font-size:16px;line-height:21px;font-family:ArialMT;color:#000000;} Finding Limits Analytically The limit of a function x approaches 3 as x approaches 3. We will call that x squared. If wegraph this, it looks something like this. And there are tick marks, but we will not worry aboutthem. The value 3 is over here and we have a point on the curve approaching 9.Let f(x) = x2. Then f(3) = 9, so the limit of f(x) as x approaches 3 is also 9. This proves that fis continuous at x = 3. When we take the limit as x approaches 3 of this function f of x, we get 3 squared is 9 plus 3is 12. 4 times 3 is 12; but when we subtract 12 from both sides, we are left with 0.In this case, we are unable to determine the limit of the function at this point. Moreinvestigation is needed.The first example will be solved by factoring. Another example is going to be solved byrationalizing, or multiplying by a conjugate. Another example can be solved using FOIL ordistributing.Algebra can be used to solve problems with an indeterminate form, in which you have a 0 inthe numerator and/or denominator.