Expert Q&A Done Limits 2: Limit Laws Model 1: Addition of Functions 10 O The thin curve represents the function f . The bold step function is g, and the extra-bold function is (f + g)(x), where (f+2)(x)= f(x)+2(x). Construct Your Understanding Questions (to do in class) 1. According to the graph of f what is a. f (1)= b. f(2) - 2. Check your answers to Question 1. Then use Model I to fill in missing entries. a f(a) lim f(x) &(a) lim g(x) (f +x)(a) 0 6 6 3 3 9 1 4 3 2 5 3 6 7 3. (Check your work) One cell in the table above is a limit that is undefined. Circle this cell. 4. Add the heading lim( f + g)(x) to the top of the shaded column, and fill in this column for a = 0, 1, 2, and 3. 5. Which two columns are related to the shaded column? Describe how they are related. 6. (Check your work) Which Limit Law in Summary Box L2.1 confirms your answer to the previous question? (If none fit, consider revising your answer to the previous question.) Summary Box L2.1: Limit Laws If lim f(x) and limg(x) exist then... Sum Law lim[ f(x) + g(x)] = lim f(x) +lim g(x) and (SL) lim[ f(x)- g(x)] = lim f(x) -limg(x) Constant lim[c . f (x)]= c. lim f(x) where c is a constant Multiple Law (CML) Product lim[ f(x)- g(x)]= lim f(x)-limg(x) Law (PL) Quotient [f (x) ] lim f(x) Law (QL) lim provided limg(x) #0 g(x) lim g(x) Limit of limx = a Identity (LId) Limit of lime = c where c is a constant Constant (LC) Natural Power Law lim[ f(x)] = lim f(x) where n is a positive integer (nPwL) Root Law lim of(x) = flim f(x) n is a positive integer, lim f(x)> 0 when n is even (nRtL) 7. What is... (For each, give the name or abbreviation of the Limit Law that confirms your answer.) a. lim x = b. lim x = c. lim12 = d. lim 12 = X-2 x-+42 E-+1000