Question

Q3

1. For the following, in (a) sketch the graphs of the functions and in (a) and (b) find the areas as indicated (a) the area bounded by y = f(x) = x2 - 4x + 5 and y = g(2) = 2x - 3. (b) the area of the region that is common to r= 3 cos(0) and r = sin(). See sketch below. 2. Consider the region bounded by y? = 4, y = 2 and r = 4. Write down the integrals needed to find the volume of the solid formed when the area is rotated about (a) the x axis and (b) the y axis by BOTH (i) the disc method and (ii) the shell method. DO NOT evaluate the integrals. 3. For the region in Question 2, find the volume of the solid formed when the area is rotated about the line r = 4. 4. Use Simpson's Rule with n=4 intervals to approximate sin(x + 1)(In(x + 1))ºda. 5. Determine if the following sequence converge w {}{usin(} ({{-1}#}. 6. Determine, giving full reasons, the convergence/divergence of r = sin(o) cos(0)

Answer 1

4x 2, and x 4 fivst draw the fque 4.4 we Reguired Volume (4,2) V= A ca d ohere 2 t4 Attp= 4 d2 -4 (2 Va 4 4 2 + 47) 12 -4 - - 18t 64 4.(2+4) - 6+ 32 12 26 Ar