MTH201 Practice Solutions Lectures 1-22 by Mathematics

Lecture No. 1

Important Note:

✓ Practice these questions on your rough notebook.

✓ Type their solutions in Math Type Software in order to increase your typing

speed.

✓ For more practice questions, follow the recommended book.

✓ Make a list of formulae of this lecture, which will help you for a quick

revision in the future.

Q1. What is the difference between quadrant and octant?

Q2. Describe two applications of Differential Calculus and two applications of Integral

Calculus.

Q3. In two dimensions, in which quadrant, are the following points located?

1. (2, 5)
2. (

3, 7)

c) (9, 2)

d) ( 8, 1)

Q4. In three dimensions, in which octant, are the following points located?

1. (1, 2, 3)
2. (

5, 7,1)

c) (9,

Q2. , 6)

1. (

9, 3, 9 )

e) ( 4, 2, 6 )

f) ( 1, 2, 3 )

g) (2, 2, 2 )

Q5. Identify the functions of single variable, two and three variables.

a) y x

b) z x y

c) w x y z

d) y x x

e) A r f) 2( P x y

Q6. Write down a function of two variables and a function of three variables.

Q7. Identify rational and irrational numbers.

5 , 3.6134613461346134….. , 9.185 ,

Answers

Q1. In two dimension plane, say xy- plane, we divide the plane into four parts. Each part

is called quadrant.

In three dimension space, we divide the whole space in eight parts. Each part is

called Octant.

Q2. See handouts lecture No. 1. The answer is there.

Q3. (a) First quadrant (b) Second quadrant (c) 4th quadrant (d) 3rd quadrant

Q4. (a) First octant (b) 2nd octant (c) 4th octant

1. 3rd octant (e) 7th octant (f) 6th octant

(g) 5th octant

Q5. (a) single variable (b) two variables (c) three variables

1. single variable (e) single variable (f) two variables

Q6. f(x,y) = 3x+4y OR f(x,y)= x2+y2 OR any function of two variables

Lectures # (2 -3)

Q1. Let

f x y x x y y . Is the function defined at the point (4 , 2)? If yes, what is its

value and if not, give the reason.

Sol:

(4,2) (4) 9(4) (2) 2(2)

1164 f x y x x y y

f

Q2. Let

xyz f x y z x ye . Is the function defined at point (1, 3, 6) ? If yes, what is its value and

if not, give the reason.

Sol:

(1)(3)(6) (1,3,6) (1) (3)e 196979907.4 xyz f x y z x ye

f

Q3. Let

f x y z such that (x, y, z) ln f x y z . Is the function defined at origin? If

yes, what is its value and if not, give the reason.

Sol: f is not defined at origin.

Q4. Find the points where the parabola, represented by the equation 𝑦= 𝑥2 −4𝑥 , meets x-axis.

Sol: See solution of Q#5.

Q5. Sol:

(after factorizing x = 2 and x = 4)

Q6. Find the mid point between (6,2,4) and (2, 5, 8).

Sol: 6+2

2 , 2+5

2 , 4+8

2 ) = ( 2 , 2 , 2 ) = (4, 2 , 6 )

Q7. Find the distance between the points

(4, 5, 9) A and (1, 3, 7) B

Solution: √(4 −1)2 + (5 −3)2 + (9 −7)2 = √17

Q8. For a line joining the points

(3, 2, 6) A and (0, 3, 4) B , find

a) Direction ratios of the line AB