MTH 162 Midterm: MTH 162 University of Rochester 162 Exam2 spr2007

• School: University of Rochester
• Department: Mathematics
• Course: MTH 162
• Professor: All

Document Summary

January 10, 2003: (10 pts) suppose that we are trying to solve x4 + x 1 = 0 using newton"s method. Assume that our rst guess was x = 1. What would the second guess be? f (x) = x4 + x 1 f (x) = 4x3 + 1 f (1) = 1 f (1) = 5. Therefore, setting x0 = 1, our second guess would be x1, where x1 = x0 f (x0) f (x0) f (1) f (1) 5: (14 pts) a cylindrical can must have a volume of 10 cubic inches. The top and bottom cost 1 cent per square inch, while the side costs 2 cents per square inch. Find the dimensions of the can which minimizes the cost. Let r be the radius of the can, and let h be the height. Since the volume must be 10, we have. The area of the top and bottom is and the cost is.