Let f(x) = ln x and let p_n and q_n be the nthorder Taylor polynomials for f centered at 1 and e, respectively. 

a. Find p₃ and q₃.

b. Graph f, p₃, and q₃ on the interval [0, 4].

c. Complete the following table showing the errors in the approximations given by p₃ and q₃ at selected points.

d. At which points in the table is p₃ a better approximation to f than q₃? Explain your observations.

Transcribed Image Text:

|In x – p:(x)|| |In x - 43(x)| х 0.5 1.0 1.5 2.5 3 3.5