Ignou Bsc Maths Assignment, Assignments of Mathematics

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ASSIGNMENT BOOKLET

Bachelor’s Degree Programme

CALCULUS

(Valid from 1

st

January, 2021 to 31

st

December, 2021)

It is compulsory to submit the assignment before filling the exam form.

School of Sciences

Indira Gandhi National Open University

Maidan Garhi

New Delhi-

(2021)

MTE- 01

Dear Student,

Please read the section on assignments in the Programme Guide for Elective Courses that we sent you

after your enrolment. A weightage of 30 per cent, as you are aware, has been earmarked for continuous

evaluation, which would consist of one tutor-marked assignment for this course. The assignment is in

this booklet.

Instructions for Formatting Your Assignments

Before attempting the assignment please read the following instructions carefully:

1. On top of the first page of your answer sheet, please write the details exactly in the following format:

ROLL NO.: ……………………………………………

NAME: ……………………………………………

ADDRESS: ……………………………………………

……………………………………………

……………………………………………

COURSE CODE: …………………………….

COURSE TITLE: …………………………….

ASSIGNMENT NO.: ………………………….…

STUDY CENTRE: ………………………..….. DATE: ……………………….………………...

PLEASE FOLLOW THE ABOVE FORMAT STRICTLY TO FACILITATE EVALUATION AND

TO AVOID DELAY.

2. Use only foolscap size writing paper (but not of very thin variety) for writing your answers.

3. Leave 4 cm margin on the left, top and bottom of your answer sheet.

4. Your answers should be precise.

5. While solving problems, clearly indicate which part of which question is being solved.

6. This assignment is valid only upto December, 2021. If you have failed in this assignment or fail to

submit it by the last date, then you need to get the assignment for the next cycle and submit it as per the instructions given in that assignment.

7. It is compulsory to submit the assignment before filling in the exam form.

We strongly suggest that you retain a copy of your answer sheets.

We wish you good luck.

ASSIGNMENT

Course Code: MTE- Assignment Code: MTE-01/TMA/ Maximum Marks: 100

1. Which of the following statements are true. Give a short proof or a counter example is

support of your answer. (10)

(a) The function f ,given by

( 6 9 6 ),

( )

3 2 f x = x − x + x + has a point of inflection.

(b) tan 6 sec ( 3 ).

2 2

3

3

2

2

t dt x x dx

d

x

= 















∫

(c) The function y = sin x is monotonic on. 2

,

2 







 −π π

(d) The graph of the function y = x −| x |lies in the 3

rd quadrant only.

(e) The tangent to the curve 2 0

2 2 x + y − x = at the point ( 2 , 0 )is parallel to the x -axis.

2. (a) If (^) y = em^ tan^ −^1 x ,show that (5)

( 1 ) 1 ( 2 ) ( 1 ) 1 0.

2

• x yn + + nx − m yn + n n − yn − =

(b) Write down the Taylor’s series for cos 4 x around zero. Hence, find out for which (5)

value(s) of (^) k the function (^) f ,given by











+ =

≠

−

= 2

k(2 sin x),whenx 0

,whenx 0

1 cos 4

( ) 2

x

x

f x

is continuous at x = 0.

3. (a) Find the length of the curve given by (^) x = et^ cos t , y = et sin t lying in (^0) ≤ t ≤π. (5)

(b) Find the derivative of cos ( 1 2 )

1 2 − x

− with respect to cos ( 1 ).

1 2 − x

− (5)

4. (a) Evaluate (^).

4 5

2

dx x x

x

∫

+ +

+

(5)

(b) Give an example of a function which is one-one when defined on a domain D 1 ⊆R,

but not when defined on a domain D 2 (^) ⊆R.Justify your choice of example. (3)

(c) Give an example, with justification, of a function with domain [ 2 , 5 ]which is not

integrable. (2)

5. (a) Find the maximum height of the curve y x x

2 2 = 4 sin − 3 cos above the x -axis. (5)

(b) Evaluate. ( 1 )( 1 )

( 4 2 )

∫ 22

+ −

−

x x

x dx (5)

6. (a) Find the intervals of (^) R, where the function (^) f ,defined by (^) ( ) 27 36 ,

3 f x = x − x + is

increasing or decreasing. (5)

(b) Prove that (5)

,

cot (^2)

/ 2

/ 4

−

π

π

−

−

= ∫ = n

n n I n

I xdx and hence evaluate I 4.

7. (a) Find the equations of the tangent and normal to the curve (5)

2 3 x = t , y = t at t = 2.

(b) Find an approximate value of ln 2 ,by solving the definite integral ,

2

1

∫

x

dx using the

Trapezoidal rule with 5 ordinates. (5)

8. Trace the curve ,

x

y = x + stating all the properties you use for doing so. (10)

9. (a) Find the area of the region bounded by the curve ( 2 ).

4 2 5 a y = x a − x (5)

(b) Graph the function f ,defined by f ( x )= | x |+| x − 1 |.Also, give its domain and

range. (5)

10. (a) Evaluate (^) [ ].

2

0

∫ x^ dx

(4)

(b) Find the derivative of

x x x x

tan cos

• (sin ) w.r.t.x. (6)