Paper 4: Fundamentals of Business Mathematics & Statistic
3.16 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Example 42 : x x x 0 lima b → x − Solution: Expression x x x ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.17 (ii) x 0limf x→ ( ) when f(x) = 1, x ³ 0. = – 1, x < 0 [Ans. doesn ...
3.18 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus If however all these values are equal, then f (x) is continu ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.19 Example 45: Discuss the continuity of f (x) at x = 4, where f(x) = 2x ...
3.20 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Example 49: Discuss the continuity at x = 2 where f(x) = 4x ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.21 (i) A function f(x) is defined as follows : f(x) = x + 1, when x ≤ 1 ...
3.22 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus If find f x( )=1 x1 x+− , [Ans.^12 ] If f(x) = x + | x | ar ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.23 3.4 DERIVATIVE Introduction : The idea of limit as discussed previous ...
3.24 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Now dxdy=δ →limx 0 δδxy=δ →limx 0f x x f x( + δδx)− ( )=h 0l ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.25 Example 50 : (^) dxd(x 4x ;^4 )=^3 dxdx 1.x= 1 1− = 1x^0 = 1.1 = 1. d ...
3.26 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus dx dxdy d= (3x 5x 110^5 −^3 + )=dxd(3x^5 )−dxd(5x^3 )+dxd.11 ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.27 Example 58: y = x (x^2 – 1) (x^3 + 2), find dydx. Let y = uvw, where ...
3.28 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus SELF EXAMINATION QUESTIONS Part A-regarding sum and differen ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.29 Part B Regarding product functions : Differentiate the following with ...
3.30 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Theorem. If y = f(z) and z = φ (x) then dy dy dzdx dz dx=. ( ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.31 Example 64 : y = log (4x), find dydx Solution:Let y = log u, where u ...
3.32 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Example 69: Given y= 2x 1x 2++ , find dydx. Solution: Let y ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.33 Example 72: y = loge (^) (x x a ,+^2 +^2 ) find dydx. Solution: Let y ...
3.34 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus log log log x^2. [Ans. 2 2 (^1). 1 2. log logx logx x] If ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.35 ( ) ( ) ( ) ( ) ( ) 3 2 2 3 32 32 dy 1 t 6at 3at 3t 3at 2 t dt 1 t 1 ...
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