MATH 106 MIDTERM 3 Please work out each of the given problems.  Credit will be based on the steps that you show towards the final answer.  Show your work. PROBLEM 1   You are constructing the newest resort at the bottom of Lake Tahoe (which is 1654 feet deep).  Your resort will feature a giant vertical circular window of radius 50 feet such that the bottom of the window lies on the bottom of the lake.  How much total fluid force will the window have to withstand?  (The density of fresh water is 62.4 pounds per cubic foot).                                                                                                                 PROBLEM 2 (17 Points) A semicircular piece of glass of constant density and radius 6 inches is to be attached to a string so that the string balances the glass perfectly.  Where should the string be attached?     PROBLEM 3  (15 Points Each) Integrate the following:     PROBLEM 4  Calculate the following limits if it exists: A. (10 Points)    Solution B. (10 Points)    Solution     PROBLEM 5 Find the following integrals if they converge.  A. (10 Points)    Solution B. (10 Points)     Solution Back to Math 106 Home Back to the Math Department Home e-mail Questions and Suggestions