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...

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 ( =
Image of page 1
Notes 1.4: Algebraic Limits Page 2 of 6 Example 5:
Image of page 2
Image of page 3

You've reached the end of your free preview.

Want to read all 6 pages?

  • Fall '14
  • Reinke

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes
A+ icon
Ask Expert Tutors