SOLUTION: a) Find all the sixth roots of (12+5i).
b) Differentiate log(3x + 7) w.r.t.
Question 2: (5 Marks)
a) Find the equation of the line joining the po
Question 277702: a) Find all the sixth roots of (12+5i).
b) Differentiate log(3x + 7) w.r.t.
Question 2: (5 Marks)
a) Find the equation of the line joining the points
(─7, 6, ─ 3) and (7, ─ 6, 3).
b) Find the equation of the sphere, which contains the circle
x2 + y2 + z2 = 18 , 3x + 3y + 3z = 11 and passes through the origin.
Question 3: (5 Marks)
a) Find the area bounded by the x-axis, the curve y = e2x and the ordinates x = 2 and x = 3. b) Prove that tan-1 x < x for all x > 0
(Using mean value theorem on {o,x} for tan-1x)
Question 4: (5 Marks)
a) Using Simpson’s rule to evaluate the following, taking n = 4
b) Find the area of the region included between the circle:
x2 + y2 + 2 x + 10y + 27 = 0
and the parabola
y2 + 10y – x + 23 = 0
Question 5:
(a) Evaluate the following: (3 Marks)
(i) dx
(ii)
(iii) dx
(b) Prove the following inequalities: (2 Marks)
(i) for all positive x.
(ii) for all x > 0.
(