NOTES 1.4 Algebraic Limits.pdf - Notes 1.4 Algebraic Limits §1.4—Algebraic Limits Finding limits without a graph or a calculator is where the fun is

# NOTES 1.4 Algebraic Limits.pdf - Notes 1.4 Algebraic Limits...

• 6

This preview shows page 1 - 3 out of 6 pages.

Notes 1.4: Algebraic Limits Page 1 of 6 §1.4—Algebraic Limits Finding limits without a graph or a calculator is where the fun is to be had. Often, this requires some traditional algebraic manipulations. We will look at a few of these methods in this section; some will be a quick review, some will be new. The names of the methods are not important, but recognizing the situations in which each method arises IS important. Example 1: Direct Substitution Always try 1 st . If you get 0 0 or , the goal is to manipulate the expression algebraically to eradicate the “bad guys” from the numerator or denominator that cause the 0 0 or . After the “bad guys” are gone, direct substitution will work. (a) 5 3 lim csc x x π = (b) lim x →- 4 - - x = Example 2: Knowing a VA exists Remember any time direct substitution yields 0 0 , there is a VA at that x -value (a) 3 1 1 lim 1 x x x + + = - (b) lim sin x x x π + = Example 3: Limits at Infinity These are easy to spot. (a) lim x →∞ 5 x 2 - 2 x + 3 - 4 x 2 1 = (b) lim x →-∞ ln x = Example 4: Piecewise Functions These, too, are easy to spot. (a) If f x ( 29 = x 2 - 3, x 2 1 2 x + 1, x 2 , lim x 2 f x ( = (b) If f x ( 29 = sin x , x π 1, x = π , lim x π f x ( =
Notes 1.4: Algebraic Limits Page 2 of 6 Example 5:

#### You've reached the end of your free preview.

Want to read all 6 pages?

• Fall '14
• Reinke

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern