In Section 8.8, it was shown that the Legendre polynomials Pn(x) are orthogonal on the interval [-1,1] with respect to the weight function w(x)=1. Using the fact that the first three Legendre polynomials are find the first three coefficients in the expansion Where f(x) is the function

2.1 The Idea of Limits distance Average velocity = time = slope of secant line Secant line – the line between two points on a graph Sparky’s average speed if he goes 8 miles in the span of 2 hours. 8mi 2hrs4mph Ex. An acrobat swings from a rope. Her displacement at time t is given by 3sint. What is her average velocity on the following intervals distance3 π = 6 [0, 2 ] time π ¿π 1.9099 2 distance ¿3sin.5 [0, .5] time .5 ~ 2.8766 distanc3sin.1 [0, .1] time = .1 ~ 2.9950