The following data is given:  x 1 2.2 3.4 4.8 6 7 y 2 2.8 3 3.2 4 5 (a) Write the polynomial in Lagrange form that passes through the points; then use it to calculate the interpolated value of y at x = 5.4 .  (b) Write the polynomial in Newton's form that passes through the points; then use it to calculate the interpolated value of y at x = 5.4 .

The volume V of an ice cream cone is given by V = where R is the common radius of the spherical cap and the cone, and h is the height of the cone. Use linearization to estimate the change in the volume when R changes from R = 1.5 inches to R = 1.7 inches, and h changes from h = 4 inches to h = 4.1 inches. Give your answer to two decimal places. R ----- h 6.20 |× in3