CALCULUS lMA - Homework Assignment #3 Due: Nov 23rd at 11:59pm {EST} on gradeacopema For full credit. ensure you show all your work and explain your reasoning. Simply stating the nal answer [or any of the following questions will not result in full credit. You should avoid using calculators and leave your answers in exact form. even in questions involving words like "approximately" you won't increase your grade by showing us the decimal expansion of your results. so don't worry about that extra step. Make sure you read and follow the submission instructions for lGrarlescope. 1. ti. Consider the function delined by re} = sin{1..r' III]. t [1 mark} State the domain of this function. i [2 marks} Determine the derivative ofsin-[1..-'|r:|}. Be careful to show all your work. _ {3 marks} Evaluate _ cosh} 1 IIEI'I] Esinr] _ 1 _ I . {3 marks] If el-{ll'lcm'z of material is available to make a box with a square base and an open top. Iind the dimensions of the box that give the largest possible volume. 1What is the maximum value of the volume'.' . {3 marks] A rectangle has its base on the zaxis and its upper vertices on the parabola y = '3 .r2. Find the maximum possible area of the rectangle. {3 marks] The following is the sketch of the graph of f{:]. Use this graph to Iind the increas ingfdecreasing intervals of 3'. points on .r-axis at which f has a local maxfmin and inflection points and the intervals on which f is concave upfdown. {3 marks} The cost of laying a bre optic cable underwater is El times that of underground. An island is 4 km from point 3 on the shore and a broadcast station. E. is 14 km along the shore. perpendicular to S. How should the cable be laid to keep cost to a minimum