{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 23 - Calculating Limits using the limit laws Limit Laws...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Calculating Limits using the limit laws Limit Laws Suppose that is a constant and the limits lim exist. Then 1. 2. 3. 4. 5. lim lim lim lim lim lim lim lim lim lim lim lim if lim lim lim and lim 112-2. lim lim d. a. lim lim lim lim lim MTH 173, section 2.3,page 1 b. c. d. e. f. lim lim lim lim lim DNE lim lim lim 6. lim lim Limits of graphs that have no holes, jumps, breaks, or gaps in them are fairly easy to calculate. The next rules exploit this idea. Two special limits Consider the function . What is lim What is lim What is lim What is lim Generalizing, we have 7. lim MTH 173, section 2.3,page 2 Consider the function lim lim lim lim so we have lim Then using 6 and 8, we have 9. lim Similarly, 10. lima and 11. lim lim a positive integer Recall that a polynomial is a function of the form , where is a positive integer and each is a real number. The domain is all reals. The graph has no breaks, jumps, gaps, or holes. So, if is a polynomial, then lim MTH 173, section 2.3,page 3 Similarly, a rational function is the quotient of polynomials. Thus, if rational function, then lim as long as 4. 8. lim lim is in the domain of . is a 12. lim lim lim 16. lim 20. lim ! DNE ! ! ! ! lim ! ! ! ! ! ! ! lim ! ! lim ! MTH 173, section 2.3,page 4 in 22, we rationalize the numerator 22. lim ! ! ! ! ! ! lim ! ! ! " lim " ! lim ! on " lim " determine lim 36. If lim This is an example of the Squeeze Theorem: If " " ! when is near , and lim then 40. lim lim lim ! , MTH 173, section 2.3,page 5 46. a. lim lim b. c. Does lim Sketch graph if if " # exist? No MTH 173, section 2.3,page 6 ...
View Full Document

{[ snackBarMessage ]}

### 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