Show that each of the following equations has a unique solution in the given interval, and use Newton's method to find it to 5 significant decimal places.

MAT 211 Lecture 6 15.3 & 15.4 Section 15.3 Homework #8: ln(x,y)= x +y2yx2 lnx= 0 & lny= 0 1st Derivative: lnx= 2xy lny= 2y2yx I. 2xy=0 > x=1 2y=0 2=y y= 2 2 2y2yx=0 > y=0 2xy =0 2x0=0 x=0 II. 2y(1x)= 0 y=0 & x=1...