Paper 4: Fundamentals of Business Mathematics & Statistic

3.28 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Calculus

SELF EXAMINATION QUESTIONS

Part A-regarding sum and difference of functions :

Differentiate the following functions with respect to x (or independent variable) : (a, b, c, m, n, are constants):

1. (i) x^7 + 7 (ii) 7x^7 + 7 [Ans. (i) 7x^6 , (ii) 49^6 ]


2. (i) ax + b + c (ii) ax^2 – bx (iii) a b4 2.x x c^4 +^2 + (iv) x^5 + bx^3 – cx.

[Ans. (i) a (ii) 2ax – b (iii) ax^3 + bx (iv) 5x^4 +3bx^2 – c]

3. (i) xm + mx (ii) xm + xm – 1
   [Ans. (i) mxm – 1 + m (ii) mxm –1 + (m – 1) xm – 2]


4. (i) x 4+ (ii) 2 x 3x+ (iii) ( )
   2
   x 1+ (iv) 4 x x( +^2 )

[Ans. (i)

1

2 x (ii)

(^13)
x

• (iii) 1 1
  x


• (iv)^2 8x
  x

+ ]

5. (i) 2x^2 +^2 x (ii)

12

x+x^ (iii) x+^1 x (iv)

1 2

x

x

(^) −
(^)
[Ans. (i) 4x−x^22 (ii) 2x−x^23 (iii) 2 x1 1−2x3/2 (iv)^1 −x^12 ]

6. (i)

3 2

2

2x 3x 4

x

+ + (ii) x 2x 1^32

x

+ −

[Ans.(i)^2 −x^83 (ii)^52 x 3 x^3 /2+ +2x^1 3/2]

7. If y = 4x^6 + 2x^3 + x - 1000, find dydx when x = - 1. [Ans. –17]


8. Ify = 4x^3 – 15x^2 + 12x + 3 = 0; find the value of x for which dydx=0. [Ans.^12 , 2]


9. If y = x. (i) prove that x dydx = 3y, (ii) find the value of
   dy^2
   1 +^ dx^ [Ans. 10]


10. Given

5 3

3

6x 3x (logx 2) 5 dy;find

x dx

− + + [Ans.

4

12x 15 3]

−x −x]