Math 1B Test#1 Directions: Name: When lets a) No notes, cell phone, calculator, or computer is allowed during the test. b) Show your work, answers alone will not count. Make use of proper notations. 1 . The graph of f is given below. If g(x) = So f(t) at, find the following value. Use the provide graph to show your work. (4 points) a ) Find 9 ( 5 ). b ) Sketch g(x ) g ( 20 ) = ( 2 ( t ) d+ 0 2 10 8 (5 ) = 1 5 . 10 = 50 25 - 1 = 24- 12 23- 011 2 2.2 . Let g(x) = Singethat ( 4 points) a. Find g'(x). 9 b . Find . 9' ( 3 ) 3 = e sinx Sin 2 e W / 2 ( singc ) at sin sing to - NO e 9 2 sing ee O sing 2 sink S e - sing - Sin 2 JC W3. Use the substitution method to find the integral. (2 points each) a. x+2 Vx2+4x dx S b. S tan x In(cos x) dx * +2 1x U = ( 2 + 4x ) 5x2+4 26 doc In Aul due C. ex+idx ex+x S x2 V2 + x dx ex + 1 doc = U= e + 26 du = of du = da S x Ju duSketch the region enclosed by the given curves and find its area. y = cos x, y = 1 - cos x on O S x ST OSketch the region enclosed by the given curves and find its area. y = cos x, y = 1 - cos x on O S x ST O5. Simply SET UP the integrals for the following problems. DO NOT evaluate. a. The integral representing the volume obtained by rotating the region bounded by the curves x = y2 + 1 and y = x - 3 about x= -1. Use the Washer Method. Provide the graph and clearly label the x and y axis, the cross section, and find the intersection(s) TT 4 + 1 - JE 26 - 3 doc y = x - 3 x=3 The integral representing the volume obtained by rotating the region bounded by the curves y = x' and y = 2x - x2 about x = -2. Use the Shell Method. Provide the graph and clearly label the x and y axis, the cross section, and find the intersection(s) 42 2x - x2 x ( 2 - 20 ) 76 =o. The base of S is the region enclosed by the parabola y = 1 - x2 and the x-axis. The cross- sections are perpendicular to the y-axis are squares. Provide the diagram and clearly label x and y axis and the cross-section. Then, compute the volume.7. Use the Shell Method to COMPUTE the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the bounded region, find the intersections, and draw the cross-section. Show every step for this problem. y = x2 +1, y= 9 - x2 about y = -1One set-up the following word problem: Provide the diagram, cross-section, and label the axis being used to analyze for the integral. Formula: W=Fxd A heavy rope, 40ft long, weighs 0.5 lb/ft and hangs over the edge of a building 110 ft high. How much work is done in pulling the rope to the top of the building