Paper 4: Fundamentals of Business Mathematics & Statistic
2.64 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Algebra Solution: 3x + y = 2 7 8 9 (i) 2x – y = 3 3 12 11 ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 2.65 (2) Find X & Y Where 3X + 2Y = −^3 1 2^7 X – Y= 81 − 96 ...
2.66 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Algebra Singular and Non Singular Matrix If detA = 0 for square matri ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 2.67 Solution: det 2 3 2 6 3 3 2 3 2 − − (^) − (^) − − − (^) = 2 det 3 3 3 ...
2.68 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Algebra Example 117 : Find the determinant of the given 3×3 matrix 6 ...
Study Note - 3 CALCULUS FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.1 3.1 FUNCTION FUNCTION : If x and y be two real ...
3.2 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Example 4 : y^2 = x. Here for every x > 0, we find two val ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.3 Algebraic function : A function in the form of a polynomial with finit ...
3.4 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Example15 : If y = x^2 + 4 is a function under consideration ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.5 2 2x , x 1 = −^1 ≤ x < 3 Find f (– 1), f(0), f (1/2), f (2). f( – 1 ...
3.6 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Show that 2 2 x 6x 8 x 8x 12 − + − + is undefined for x = 2 ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.7 ]c , c [ , 0− ∈ + ∈ ∈ > Is the neighbourhood of c. Any neighbourhoo ...
3.8 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus (ii) Method of substitution (iii) Method of rationalization. ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.9 ( 1) 2 =^ + − +^ n L (^) a n n n h a a ∴ Lt→ Lt→ 0 ( 1) 2 − = (^) + − ...
3.10 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Solution: Now 2 2 ( 1)(2 3) 2 5 3 ( 2)(3 4) 3 10 8 + + = + + ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.11 And (^) x 0lim f(x) lim|x| lim( x) 0.→ − =x 0→ − =x 0→ −− = ∴ limf(x) ...
3.12 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus (i) f(a) does not exist, but x alim f x→ ( ) exists. (ii) f( ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.13 Example 33 : Evaluate 2 x 1 2 limx 3x 2. → x 4x 3 − + − + Reqd. limit ...
3.14 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Example 36 : Find 2 x^2 lim 5 2x. → ∞3x 5x − + Solution: Exp ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.15 Example 39 : Evaluate (i) x 0 lim4x |x| → 3x |x| + + (ii) x 2 lim|x 2 ...
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