12/30/2019 0 Comments
Pre Calculus Mod 5 - Assignment Example f(X) =ex3 f '(x) = 3x2 ex3 d. f(X) =2X2 e (1-X2) r (x) = 2x2, r' (x) = 4x s(x) = e (1-X2) s' (x) = -2 e (1-X2) Applying product rule, f '(x) = 2X2-2 e (1-X2) + 4x e (1-X2) = -8x2 e (1-X2) + 4x e (1-X2) = (4x -8x2) e (1-X2) e. f(X) =5X e (12-2x) Let r(x) = 5x, r' (x) = 5 and s(x) = e (12-2x), s' (x) = -2 e (12-2x) f '(x) = 5x (-2 e (12-2x)) + 5 e (12-2x) f '(x) = -10x e (12-2x) + 5 e (12-2x) = (-10 + 5) e (12-2x) f. f(X) =100e(x8 + x4) f '(x) = 8x7 + 4x3e(x8 + x4) g. f(X) = e (200X-X2 + x^100) f '(x) = 200 â€“ 2x + 100x^99 e (200X-X2 + x^100) 2. Find the derivatives for the following functions: a. f(X) = ln250X b. f(X) = ln (20X-20) c. f(X) = ln (1- X2) d. f(X) = ln (5X + X-1) e. f(X) = Xln (12- 2X) f. f(X) = 2Xln(X3 + X4) g. f(X) = ln (200X - X2 + X100) Solutions The derivative of the function y = ln x is obtained by d/dx (ln x) = 1/x. d/dx logex = 1/x, suppose y = ln x, then dy/dx = 1/x a. f(X) = ln250X log ab = log a + log b Therefore, the equation can be rewritten as f (x) = ln 250 + ln x d/dx ln 250 = 0 (derivative of a constant) d/dx (ln x) = 1/x Hence dy/dx = 1/x. b. f(X) = ln(20X-20) If y = ln u and u is some function of x, then dy/dx = u'/u If y = ln f(x), then dy/dx = f ' (x)/ f(x) Let u = 20x â€“ 20 u' = 20 dy/dx = 1. u'/u = 20/(20x â€“ 20) c. f(X) = ln (1- X2) Let u = (1- X2) Then u' = -2x dy/dx = 1. ... ln (12-2x) f ' (x) = 2x/ (12 â€“ 2x) + ln (12-2x). f. f(X) = 2X ln(X3 + X4) Let r(x) = 2x, therefore, r' (x) = 2 Similarly, if s(x) = ln (X3 + X4), s'(x) = (3x2 + 4x3)/ (X3 + X4) Therefore, f ' (x) = 2x ((3x2 + 4x3)/ (X3 + X4)) + 2 ln (X3 + X4) g. f(X) = ln(200X - X2 + X100) u = ln (200X - X2 + X100) u' = 200 -2x + 100x99 f ' (x) = dy/dx = u'/u = 200 -2x + 100x99/ (200X - X2 + X100) 3. Find the indefinite integrals for the following functions a. f(X) = e6X = ? e6X dx = 1/6e6X + C b. f(X) = e (5X-5) = 5/2 x2-5x e (5X-5) c. f(X) = 5eX = ? 5eX dx = 5 ? eX dx = 5eX + C d. f(X) = 1/ (1 + X) = ln ?1 + x? + C e. f(X) = 5/X = 5 integral [1/x] dx = 5 ln ?x?+ C 4. Find the definite integrals for the following functions a. f(X) = e2X over the interval [2, 4] =Integral 42 [ e2x ] dx = [ 1/2 e2 ( 4) + C ] - [ 1/2 e2 ( 2 ) + C ] = 1/2 [ e8 - e4 ] b. f(X) = 2eX over the interval [0, 2] =Integral 20 [2eX] dx = [e2 + C] - [e0 + C] = e2 â€“ e0 d. f(X) = 2/ (2 + X) over the interval [2, 5] Let u = 2 + x, when x = 2, u = 2 + 2 = 4 and when x = 5, u = 2 + 5 = 7 = ln [?2 + x?] 52 = ln (7) â€“ ln (2) e. f(X) = 10/X over the interval [3, 10] =dx = 10 integral [ 10 / x ] dx = 10 [ ln | x | ] + C, so Integral103 [ 10/ x ] dx = [ 10 ln | 10 | + C ] - [ 10 ln | 3 | + C ] = 10 ln 10 â€“ 10 ln3 = 10 [ln10 â€“ ln 3] Part2: Application of Calculus in Business Decision-Making Calculus is extensively used in making business decisions, which are critical for the success and survival of every business enterprise. Derivatives have wide applications in the business world. Derivatives are used to measure rate of change of a function in relation to the changes in variables (inputs) under focus. At some given value of an input, the derivative tells us the linear estimate of the function, which is close to
Global Communications For US Brands Like Abercrombie and Fitch - Essay Example
Some important rights of the consumer are: 1) the right to choose, 2) the right accurate information, 3) the right to safety and 4) the right to value for money. Being a meticulous consumer, the British customers know where and how to get the best value for their money, and they usually know who to approach when things go wrong. It is essential for any organization who wishes to penetrate the British market, that value does not always mean the â€œcheapestâ€ or the â€œmost expensiveâ€. It means that the consumersâ€™ perception of it is if the standard or quality is commensurate with the price of the commodity. In the end, it is normally up to the customer to decide whether the price of the goods they are willing to purchase is worth it.
(ii) In order to have a competitive advantage; A&F must incorporate the three (3) Cs or the Strategic Triangle by Ohmae. The three Cs are customer, corporate and competitor. In any business strategy, the organizationâ€™s primary concern should be its customers. Thus, it is recommended that management should implement an advertising strategy that could reach a larger portion of the market in order to edge out the competitor and penetrate more potential household consumers. However, before launching an entry into any new place, territory or country it would be best to assess the needs and wants of the target market and to know how far the competitor has come.
The best advertisement campaign recommended will be a combination of the public information model where media and local press releases will be used extensively to inform the public of the A&F presence and to build wholesome image of whole organization; and the two-way symmetrical model which is a two way communication between the company and the public to sort out conflicts...
Write something about yourself. No need to be fancy, just an overview.