________________ Lab\t3B\tWorksheet\t-\tSpring\t2017 Name:\t____________________________________ Total\tPoints:\t38 1. a. (3\tpoints)\tUse\tGeogebra\tto\tsketch\tthe\tgraph\tof f ( x) 0.4e0.4 x 2 by\ttyping\tf(x)=0.4e^(0.4x)+2\t.\tCopy\tthe\tgraph onto\tthe\tgrid\tto\tthe\tright. Shade\tthe\tarea\tbetween\tthe\tgraph\tand\tthe xaxis\ton\tthe\tinterval\t[5,\t6]. b. (8\tpoints) Now\tuse\tupper\tand\tlower\tsums\tto\testimate\tthe\tarea under\tthe\tcurve\ton\tthe\tinterval\t[5,\t6]\tand\tfill\tin\tthe\tchart\tbelow. For instance,\tto\tfill\tin\tthe\tfirst\tbox,\ttype\tLowersum[f,5,6,5]\t,\tnoticing\tthat the\tsecond\tand\tthird\titems\tin\tthe\tbrackets\tindicate\tthe\tinterval endpoints,\twhile\tthe\tfourth\tnumber\tindicates\tthe\tn\tvalue. The number\tthat\tGeoGebra\tsays\t\"a\t=\"\tis\tthe\ttotal\tof\tthe\tareas\tof\tthe rectangles,\tand\tcan\tbe\twritten\tin\tthe\ttable. Once\tyou\thave\tcomputed the\t4\tlower\tsums,\tchange\tthe\tword\tLowersum\tto\tUppersum\tin\tthe command.\tFinish\tcompleting\tthe\ttable\tbelow,\twriting\tyour\tanswers\tto\ttwo\tdecimal\tplaces: Lower\tSum Upper\tSum n=5 n=10 . n=50 n=100 c. (\t1\tpoint) After\tlooking\tat\tthe\tvalues\tin\tthe\ttable,\tmake\tyour\town\testimate\tas\tto\twhat\tthe\tactual\tarea\tis. Estimated\tarea = ________ d. (\t3\tpoints) Type\tin\tthe\tfunction\tagain\tby\ttyping\tf(x)=0.4e^(0.4x)+2\tfollowed\tby\t\"enter\". Then\ttype Integral[f,5,\t6]. Now\tthe\tnumber\tthat\tGeoGebra\tsays\t\"a\t=\" will\tbe\tyour\texact\tarea. Fill\tin\tthe\t2\tboxes and\tthe\tline\tbelow. Exact\tArea\t= (0.4e0.4 x 2)dx _________ 2. a. (3\tpoints)\tUse\tGeogebra\tto\tsketch\tthe\tgraph\tof f ( x ) 1 2 x 5 2 . Copy\tthe\tgraph\tonto\tthe\tgrid\tto\tthe\tright. Shade\tthe\tarea\tbetween\tthe graph\tand\tthe\txaxis\ton\tthe\tinterval\t[3,\t5]. b. (8\tpoints) Now\tuse\tupper\tand\tlower\tsums\tas\tin\tquestion\t1\tto estimate\tthe\tarea\tunder\tthe\tcurve\ton\tthe\tinterval\t[3,\t5].Then\tfill\tin the\ttable\tbelow\twriting\tyour\tanswers\tto\ttwo\tdecimal\tplaces: n=5 Lower\tSum Upper\tSum n=50 n=100 c. (1\tpoint) After\tlooking\tat\tthe\tvalues\tin\tthe\ttable,\tmake\tyour\town\testimate\tas\tto\twhat\tthe\tactual\tarea\tis\t. Estimated\tarea = ________ d. (3\tpoints) Use\tthe\tmethod\tgiven\tin\t1d along\twith\tGeogebra\tto\tcalculate\tthe\texact\tarea. Then\tfill\tin\tthe 2\tboxes\tand\tthe\tline: n=10 Exact\tArea\t= 1 2 x 2 dx _________ 5 3. a. (3\tpoints) Use\tGeogebra\tto\tsketch\tthe\tfunction f (x) 0.1x3 2.5x on\tthe\tgrid\tat\tthe\tright. Shade\tthe\tarea between\tthe\tgraph\tand\tthe\txaxis\ton\tthe\tinterval\t[5,\t5]. b. (3\tpoints) Use\tthe\tmethod\tgiven\tin\t1d along\twith Geogebra\tto\tcalculate\tthe\texact\tarea. Then\tfill\tin\tthe\t2 boxes\tand\tthe\tline: Exact\tArea\t= 3 0.1x 2.5x dx _________ c. (2\tpoints)\tWhy\tdo\tyou\tthink\tyou\tgot\tthe\tanswer\tabove