MTH301 Solved Papers

EXAMINATION

MTH301Calculus II

Q1.  is an example of ----------- (1 marks)

1. Irrational numbers
2. Rational numbers
3. Integers
4. Natural numbers

Q2. Straight line is a special kind of ---------------- (1 marks)

1. Surface
2. Curve
3. Plane
4. Parabola

Q3. An ordered triple corresponds to ----------- in three dimensional space. (1 marks)

1. A unique point
2. A point in each octant
3. Three points
4. Infinite number of points

Q4. The angles which a line makes with positive x ,y and z-axis are known as ------------ (1 marks)

1. Direction cosines
2. Direction ratios
3. Direction angles

Q5. Is the function (1 marks)

f x y continuous at origin? If not, why? sin3 f x y xy x y

f x y is continuous at origin

(0, 0) f

(0, 0) f (0, 0) lim x y f x y What are the parametric equations that correspond to the following vector equation? sin (1 cos2 ) r t t i t j

sin 1 cos 2 x t y t z

sin 1 cos2 y t x t z

sin 1 cos2 x t y t z

sin cos 2 x t y t z

Q9. Is the following vector-valued function (1 marks)

r t continuous at t  ? If not, why? (4cos , , 4sin ) r t t t t

(0) r

(0) r lim t r t

(0) r lim t r t exists but these two numbers are not equal.

r t is continuous at t 