STUPIDSID
1(a)
Using Taylor's series, find y(0.4) where dy/dx = 1 + xy with y(0) = 2.
3 M
1(b)
Find the complementary function of
3 M
1(c)
Evaluate the following:
3 M
1(d)
Evaluate the following:
3 M
1(e)
Show that the following holds true:
4 M
1(f)
Using Euler's method, solve: dy/dx = x + y, y(0) =1. Find the value of y at x=1, taking h = 0.2
4 M
2(a)
Evaluate the following:
6 M
2(b)
Use Runge-Kutta method of fourth order to solve dy/dx=1/(x+y); y(0)=1. Find y(0.2) with h=0.1
6 M
2(c)
Solve the following:
8 M
3(a)
Solve the following:
6 M
3(b)
Solve the following using variation of parameters.
6 M
3(c)
Evaluate the following:
and hence deduce that:
and hence deduce that:
8 M
4(a)
Solve the following: (xy3+y)dx+2(x2 y2+x+y4 )dy=0
6 M
4(b)
Solve the following: 
6 M
4(c)
Solve the following: 
8 M
5(a)
In a circuit containing Inductance L, Resistance R, and Voltage E, the current i is L di/dt+Ri=E. Find i at time t. At t=0,i=0, L,R,E are constants.
6 M
5(b)
Change the order of integration:
6 M
5(c)
Evaluate the following
over the volume of a sphere x2 + y2 + z2 = a2
over the volume of a sphere x2 + y2 + z2 = a2
8 M
6(a)
Find the length of the parabola x2 = 4y which lies inside the circle x2 + y2 = 6y.
6 M
6(b)
Change into polar and evaluate: 
6 M
6(c)
Evaluate the following
over the area of the triangle formed by x = 0, y = 0, x + y = 1.
over the area of the triangle formed by x = 0, y = 0, x + y = 1.
8 M
7(a)
Change the order of integration and evaluate
6 M
7(b)
Find the area outside the circle r=a and inside the cardioid r=a(1+cosθ)
6 M
7(c)
Find the volume common to the cylinders: x2 + y2 = a2, x2 + z2 = a2
8 M
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