Paper 4: Fundamentals of Business Mathematics & Statistic
3.56 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus If y = 5x find 2 d ydx 2 [Ans. 5x (log 5) (^2) ] If f(x) ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.57 3.5 INTEGRATION Definition: For differential caculus we know. dxd(x 2 ...
3.58 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Example 114: ∫(x^4 ± x) dx = x^4 dx ± xdx (B) A constant fac ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.59 (ii) 100 x100 1 x^101 x dx 100 1 101 c + = + = + (iii) x x1 1^2 xdx 1 ...
3.60 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus (iv) (a x) dx+^2 = (a 2ax x )dx a dx 2a xdx x dx^2 + +^2 =^2 ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.61 (ii) ( ) x 22 dx x + 2 2 1/2 1/2 1/2 1/2 x 4x 4dx x dx 4 dx 4x dx x x ...
3.62 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Example 126:If dxdy=x 3x 1^3 −^2 + and y = 2 when x = 1, fin ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.63 (i) x2xdx (ii) e-4xdx (iii) e–mxdx (iv) e2logx (v) emlog x dx e^2 x ...
3.64 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Agian let x = φ (z), Then dxdz=φ ′ (z)., (change of variable ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.65 Example 130: (2x 5 dx+ )^3 Let, 2x + 5 = u 2. dx = du dx = 21 du I = ...
3.66 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Example 133: dx (^) 2 5x+ Let 2 + 5x = u 5.dx = du dx = 51 d ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.67 Example 137: x x x x e e dx e e − − − (^) + Let e x +e–x = u, (ex –e– ...
3.68 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Example 142: ex (^) x(1 xlogx)dx,x 0.+ > I e logx dxx^1 x ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.69 ( ) x x x x x log 1^1 log e 1 loge log e 1 c. e e = −^ +^ = −^ +^ = − ...
3.70 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus 3.5.2 INTEGRATION BY RATIONALISATION In some cases rationali ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.71 x 3x 7 dx(^2 + )^7 ( ) Ans. 3x 7^128 48 (^) + 2 xdx (^) 3x 4+ 3x ...
3.72 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus [Hint. I = x/2 x/2 e dx e 1 − (^) − + , put e–x/2 + 1 = u &a ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.73 (B) (^) a x 2 dx 1 a x− 2 =2a a xlog +− ,(x a)< (c) 2 2 (^22 ) dx ...
3.74 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus 1 1 1. (^2) du 1 du 1 2du 2 5 u 2 2u 1 10 u 2 10 2u 1 =^ −^ ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.75 INTEGRATION BY PARTS Integration of a Product: Let u and v 1 be diffe ...
«
5
6
7
8
9
10
11
12
13
14
»
Free download pdf