Paper 4: Fundamentals of Business Mathematics & Statistic
3.36 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Example 76 : If y = x^4 , find 2 2 d y. dx Solution: 4 3 2 3 ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.37 Solution: Y = x log x D.w.r. to x dy dx = x × 1 x + log x.1 dy dx = 1 ...
3.38 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus FOR IMPLICIT FUNCTION AND PARAMETRIC FORMS : Example 82 : Fo ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.39 SELF EXAMINATION QUESTIONS Find 2 2 d y dx^ in the following cases : ...
3.40 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Example 85 : u = (x + y)^2 = x^2 + 2xy + y^2 , u 2x 2y, 2x 2 ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.41 Now differentiating u w.r.t.x (treating y as a constant) we find fy u ...
3.42 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Example 94 : Find the first partial derivatives of f(x, y, z ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.43 SELF EXAMINATION QUESTIONS fx, fy for the following f(x, y) : (i) ( ...
3.44 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus LAGRANGES METHOD MULTIPLIERS : To find the extreme of a diff ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.45 Again x + y – 10 = 0 .... (iii) solving (i), (ii), (iii) we get x = 5 ...
3.46 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Since dydx is continuous function of x it can change sign on ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.47 Analytical Expression : Let α – h, α, α + h be the three values of x ...
3.48 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Find 2 2 d y. dx Put x = a in 2 2 d y, dx if 2 2 d y dx at x ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.49 Application : Few terms : The term marginal cost indicates the change ...
3.50 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Marginal Revenue : For any demand function p = f (q), the to ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.51 Solution: Profit (P)= Sale – total cost = x × p – y = x (300 – 2x) – ...
3.52 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Hence the maximum profit is obtained by putting x = 3 in the ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.53 Example 112 :The sum of two numbers is 12. Find the maximum value of ...
3.54 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Calculus Show that f(x) = x^3 – 3x^2 + 6x + 3 has neither maximum no ...
FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.55 A firm produces x units of output per week ata a total cost of ` 3 2 ...
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