Question 4 ( 2 Marks) The graph of the equation from A to B is revolved...
1) Find the arc length for the following curves. a. y2 = 4(x + 4)3, b. x= 0<x<2 1 sys2 + 4y2 2) Find the surface area resulting from the rotation of the curve about X axis a. 9x = y2 + 18, b. y = V1 + 4x, 2<x< 6 1<x<5 3) Find the surface area resulting from the rotation of the curve about th Y axis. a, y = 1- x2 0 SX S1
3. (a) If the region sketched in (1) above is revolved about the line y -0 (x-axis), sketch and label the typical rectangle(s) needed to use the shell method to find the volume of the resulting solid. (b) Use the shell method to find the volume of the resulting solid 2 pts [9 pts] 4. (a) If the region sketched in (1) above is revolved about the line x-O。-axis), sketch and label the typical rectangle(s) needed to use the disk/washer...
1. For the following equation, find the center, vertices, foci, transverse axis, and asymptotes, and sketch the graph: 2. Consider the set of parametric equations (a) Graph in the following window: TMIN--3.74, TMAX- 3.74, TSTEP = 0.02, XMIN =-10, XMAX = 10, YMIN =-7, YMAX = 7, Sketch the graph. (b) At, find (x, y) and dy/dx. Write the equations of the lines tangent to and normal to the graph at (c) Find the length of the curve from to...
3. Graph the region bounded by the parametric curve x cost and y = et where 0 t Find the length of the curve. b. Find the surface area of revolution when the region is revolved around the y -axis. a.
3. Graph the region bounded by the parametric curve x cost and y = et where 0 t Find the length of the curve. b. Find the surface area of revolution when the region is revolved around the y...
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Sample Test 4 1575 Calculus II 1. The region bounded by the parabola y-4x-x and the x -axis is revolved about thex- axis. Find the volume of the solid. Write answer in term of π. Find the area enclosed by the curves: 2. y=2x2-4x-12 y=x2-6x+12 and 3. Find the volume of the solid obtained by rotating the region bounded by the graphs of a. y-x-9, y 0 about the x-axis. -1 about the x-axis. b. y 16-r, y-3x+...
Find the area of the surface generated when the given curve is revolved about the given axis. y 8x, for 33sxs 65; about the x-axis The surface area is square units. (Type an exact answer, using a as needed.)
Find the area of the surface generated when the given curve is revolved about the given axis. y 8x, for 33sxs 65; about the x-axis The surface area is square units. (Type an exact answer, using a as needed.)
QUESTION 8 The region enclosed by the curves y=x3, y=0, and x = 2 is revolved about the x-axis. What is the volume of the resulting solid? O 32 - TT 3 96 5 TT 0 471 128 TT 7 64 TT
4. Refer to the graph as shown in Figure A4, determine (a) the second moment of area about x axis (Ix): (4 marks) (b) the second moment of area about y axis (Iy); (4 marks) c) the second moment of area of about z (Iz), where z axis is perpendicular to x and y axes. (2 marks) 5 y = 1.25x X 4 Figure A4 5. 1 Given the differential equation: dy +-y 3x2 dx х Find (a) the general...
Find the area of the surface generated when the given curve is revolved about the x-axis. x3 1 1 y = + 12 for 2 sxs1 х The area of the surface is square units. (Type an exact answer, using it as needed.)
1. The area between the part of the curve-6x 8 above the x-axis and the x-axis itself is 2. The area below y 4x -x and above y 3 (for1 xS 3) is revolved around the x-axis. 3. The areas between the following portions of curves and the x-axis are revolved around the revolved by an angle 2π around the x-axis. Find the volume swept out. Find the volume swept out. y-axis. Find the volume swept out. (a) y- betweenx...