MATH-1325-PHW_09, 2022-10-21 23:32 3 1. (10 points) An open box will be made by cutting a square from each corner of a 16inches by 10inches piece of cardboard and then folding up the sides. What size square should be cut from each corner in order to produce a box of maximum volume? What is that maximum volume? The dimension of the square is: , and the maximum volume is: (You must include appropriate units.) MATH-1325-PHW_09, 2022-10-21 23:32 4 2. (10 points) A farmer is constructing a rectangular pen with one additional fence across its width. Find the maximum area that can be enclosed with 720 yards of fencing. (You must use calculus to get any credit.) length 11119.1(" The maximum possible area is: (You must include appropriate units.) MATH-1325-PHW_09, 2022-10-21 23:32 5 3. (10 points) If the price charged for a laptop is [)(53) dollars Where p(3:) Z 0, then a: laptops will be sold in a certain store, Where w : 700 . 17(58) 6 (a) Find an expression for the total revenue from the sale of a: laptops. (b) Find the value of .7: that leads to maximum revenue. (c) Find the maximum revenue. MATH-1325-PHW_09, 2022-10-21 23:32 6 4. (10 points) Approximate a solution of the equation x2 - 3x + 1 = 0 on [2, 3] using the Newton's method. Write your final answer to the nearest hundredth. (You must use Newton's Method for credit.) FINAL ANSWER:MATH-1325-PHW_09, 2022-10-21 23:32 7 5. (10 points) Approximate a solution of the equation 2 - 3 In x = 0 on [1, e] using the Newton's method. Write your final answer to the nearest thousands. FINAL ANSWER:MATH-1325-PHW_09, 2022-10-21 23:32 8 6. (10 points) Approximate v19 to the nearest thousandth using the Newton's method. You must use Newton's Method for credit.) FINAL ANSWER:MATH-1325-PHW_09, 2022-10-21 23:32 9 7. (10 points) Find the following limits, using L'Hospital's rule when applicable. (a) lim 3x2 - 10x + 4 20 - 5 2 2 - 25 FINAL ANSWER: (b) 4x3 - 64x lim 2 +4 2 - Vx FINAL ANSWER (c) e220-3 lim 20 -+00 2 2 + 5 FINAL ANSWER:MATH-1325-PHW_09, 2022-10-21 23:32 10 8. (10 points) Find the following limits, using L'Hospital's rule when applicable. (a) ex- -4 - 1 lim 20->2 202 - 3xc + 2 FINAL ANSWER (b) 7x - 9 lim 2 -co In (x2 + 5) FINAL ANSWER:MATH-1325-PHW_09, 2022-10-21 23:32 11 9. (10 points) Find the following limits, using any valid method. (a) lim V9x + 5 20 -700 203 + 2 FINAL ANSWER: (b) lim V9x + 5 10-too V4x + 8 FINAL