Paper 4: Fundamentals of Business Mathematics & Statistic
3.76 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Example 158:elog x dx = logx.1.dx logx dx dlogx dx dx dx = − ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.77 (^1) u 4 du (^221) u 4 du 2 2 = 5 + = 5 + ( ) 1 u u 4 4^22222 5 2 2 l ...
3.78 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus log (x^2 + 2x + 1) [Ans. x log (x^2 + 2x + 1) – 2x + xlog ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.79 is denoted symbolically by a b f(x)dx i.e., a n (^) bf(x)dx limh f(a ...
3.80 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus h 0 limh a(b a) (b a)(b a h) → 2 =^ − + − − +^ ( ) ( ) ( ) b ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.81 Definite Integral In the previous part ( ) b a f x dx has been define ...
3.82 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Example 166: 01 2xdx 2 xdx.= 01 (^) ab f x g x dx f x dx g ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.83 Example 171:Evaluate : 2 2 1 x 2x 5dx. x + + 2 2 2 (^11) I x 2 dx^5 x ...
3.84 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus SELF EXAMINATION QUESTIONS Evaluate : (i) 2 1 0 x 2 (^) (i ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.85 3.5.6 METHOD OF SUBSTITUTION Rule of evaluate ( ) b (^) af xdx by the ...
3.86 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Example 178: (^22) x 1/x 1 2 x 1e dx. x (^) − (^) + (^) Let ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.87 (i) 1 0 dx. (^) x x+ [Ans. 2 log 2] (ii) a (^022) xdx. (^) a x− [An ...
3.88 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus If now h → 0 +, then n → ∞. ∴ ( ) 1 n 0 n r 1 f x dx lim1 r. ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.89 Example 182:Evaluate : h Lt^11 ....^1 → ∞ 1 2n 2 2n n 2n (^) + + + (^ ...
3.90 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus 3.5.7 GEOMETRICAL INTERPRETATION OF A DEFINITE INTEGRAL ( ) ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.91 So hf (a) → 0, and hf (b) → 0 as h → 0. From Eq. (1) we get ( ) ( ) ( ...
3.92 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Now area P 1 Q 1 Q 2 P 2 P 1 = area P 1 R 1 R 2 P 2 – area Q ...
Section - B STATISTICS ...
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Study Note - 4 STATISTICAL REPRESENTATION OF DATA FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 4.1 4.1 DIAGRAMATIC REPR ...
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