Fe Review Course

1. Equation of the line passing through (-1,1) and (0,3) is:

y = mx + b;         m = (y2 – y1)/(x2 – x1) = (3 – 1)/[0 – (-1)] = 2

b = y2 – mx2 = 3 = 3 – 2(0) = 3;                y  = 2x + 3                 Answer C

2.   Center of the circle is:

x2 + y2 – 8(x + y) = -4;        rewrite as, (x – 4)2 + (y – 4)2 – 16 -16 = -4

(x – 4)2 + (y – 4)2 = 28;                center is located at (4,4)        Answer D

3.   The determinant is found by expanding along the second row:

D = (1)(1 x 5 – 2 x 3) = -1                                                Answer B

1. Find the general solution to y’ + 3y = 0;          

the characteristic equation is, m + 3 = 0 thus m = -3 and y = C1e-3t;        

y(0) =1 yields C1 = 1;                                y =  e-3t                        Answer D

1. Calculate the limit as x → ∞:

divide the numerator and denominator by the highest power x3 

and taking the limit yields,

3/6 = 1/2                Answer B

1. The following trigonometric relation is valid:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

sin(a + a) = sin(2a) = 2sin(a)cos(a)                                        Answer C

1. The area bounded by y = x2 and x = y/3:

Area = ∫ (y1 – y2)dx =  ∫ (x2 – 3x)dx

y1 = y2;                         x2 – 3x; → x =3

[pic 1]        Answer D

1. The inverse Laplace transform is found by:

              [pic 2]