Use the Newton backward-difference formula to construct interpolating polynomials of degree one, two, and three for the following data. Approximate the specified value using each ofthe polynomials. a. /(0.43) if/(0) = 1, /(0.25) = 1.64872, /(0.5) = 2.71828, /(0.75) = 4.48169 b. /(0.25) if /(-I) = 0.86199480, /(-0.5) = 0.95802009, /(0) = 1.0986123, /(0.5) = 1.2943767

1.3 & 1.4 Notes Summary 1.3 – The limit of a Function The limit tells us the behavior of the function as it approaches the limit value. For example, n lim 1+ 1 n→4( ) n As n approaches 4, we can determine the behavior the function will have. Examples: 2 lim x −x+2 =4 x→2 x−1 1 lim 2 = x→1 x −2 2 lim sin x=1 x →0 x 1.4 Calculating Limits using Limit Laws lim [ (x)+g (x)]lim f (x)+lim g(x) 1. x →a x→a x→ a 2. lim [ (x)−g (x ]=lim f (x)−lim g(x) x →a x→ a x →a lim [ f(x ]=c∗lim f (x) 3. x →a x→a lim [ (x)g x ]=lim f (x)∗lim g(x) 4. x →a x→a x→ a