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

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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 ...
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