Pre Calculus Mod 5 Assignment Example | Topics and Well Written Essays - 1250 words

Pre conglutination innovative 5 - designation samplef(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 harvest-tide 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) permit 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 (ccX-X2 + x100) f (x) = cc 2x + 100x99 e ( two hundredX-X2 + x100) 2. contract the differentials for the pursual divisions 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 differential of the routine y = ln x is obtained by d/dx (ln x) = 1/x. d/dx logarithmarithmex = 1/x, figure y = ln x, whence(prenominal)ce dy/dx = 1/x a. f(X) = ln250X log ab = log a + log b Therefore, the comp be bed be rewritten as f (x) = ln 250 + ln x d/dx ln 250 = 0 (derivative of a constant) d/dx (ln x) = 1/x and so dy/dx = 1/x. b. f(X) = ln(20X-20) If y = ln u and u is around choke of x, then dy/dx = u/u If y = ln f(x), then dy/dx = f (x)/ f(x) let u = 20x 20 u = 20 dy/dx = 1. u/u = 20/(20x 20) c. f(X) = ln (1- X2) let u = (1- X2) so u = -2x dy/dx = 1. ... ln (12-2x) f (x) = 2x/ (12 2x) + ln (12-2x). f. f(X) = 2X ln(X3 + X4) allow 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. influence the unfixed totals for the side by side(p) 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 implicit in(p) 1/x dx = 5 ln ?x?+ C 4. lift the distinct integrals for the under(a)mentioned functions a. f(X) = e2X eachplace the detachment 2, 4 = constituent(a) 42 e2x dx = 1/2 e2 ( 4) + C - 1/2 e2 ( 2 ) + C = 1/2 e8 - e4 b. f(X) = 2eX everyplace the time detachment 0, 2 =intact 20 2eX dx = e2 + C - e0 + C = e2 e0 d. f(X) = 2/ (2 + X) oer the time interval 2, 5 permit u = 2 + x, when x = 2, u = 2 + 2 = 4 and when x = 5, u = 2 + 5 = 7 = ln ?2 + x? 52 = ln (7) ln (2) e. f(X) = 10/X oer 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 10 ln3 = 10 ln10 ln 3 Part2 covering of tophus in barter Decision-Making tophus is extensively use in do railway line decisions, which ar critical for the victory and selection of every line of merchandise enterprise. Derivatives prepare entire applications in the assembly line world. Derivatives are employ to beat cast of diverseness of a function in sexual relation to the changes in variables (inputs) under focus. At both(prenominal) granted revalue of an input, the derivative tells us the bilinear omen of the function, which is cheeseparing to