J-J, f(x)--3, g : S → J, g(s) = nuniber of elements in the string 's', if is even. h : J-J, h(1)- r r if is...
(a) Determine algebraically whether the functions below are even, odd or neither. i. r+6 f(x)=- r-r? (2 marks) ii. f(x) = 2x sinx (2 marks) (b) A periodic function is defined by: f(x) = 4-x?, -25x52, f(x+4)= f(x) i. Sketch the graph of the function over -10<x<10. (4 marks) ii. Based on result in (i), identify whether the function is even or odd. Give your reason. (2 marks) ii. Calculate the Fourier series expansion of f(x). (12 marks) (c) An...
4. R(A, B, C, D, E, F, G, H, I, J) where A → B, C, D BE F→ G, H, I (A, F) → B, C, D, E, G, H, I, J For each of the following relations, normalize it into a set of BCNF relations.
Please Answer ALL PARTS 3. f(r) = { 1/2 if z is even; 2x if r is odd. The domain is the set of all positive (non-zero) integers and the co-domain is the set of all positive (non-zero) integers.
(8) Let E C R" and G C R" be open. Suppose that f E G and g G R', so that h = go f : E → R. Prove that if f is differentiable at a point x E E, and if g is differentiable at f (x) E G, then the partial derivatives Dihj(x) exist, for all and j - ...., and 7m に! (The subscripts hi. g. fk denote the coordinates of the functions h, g....
1. Assume that S is an open subset of R", and that f, g: S R" are functions of class C in S. Prove that := f.g : S R is of class C, and that - D g) (Df)'g + (Dg)t (8) where T denotes "transpose." 1. Assume that S is an open subset of R", and that f, g: S R" are functions of class C in S. Prove that := f.g : S R is of class...
6. (a) If f(x a) for -al R, show that i-0 fO(a) fori 0,1,2, (where f0 (a) f(a), and fori 1 f(a) denotes the i-th derivative of f at a). (b) If f e* , find f(2014) 6. (a) If f(x a) for -al R, show that i-0 fO(a) fori 0,1,2, (where f0 (a) f(a), and fori 1 f(a) denotes the i-th derivative of f at a). (b) If f e* , find f(2014)
1. If fand g are both even functions, is the product fg even? If f and g both odd functions, is fg odd? What if f is even and g is odd? Justify your answers. (10 points) Find the domain g(x) =-. (10 points) 2. of the composited function fog, where f(x)=x+ and x +1 x+2 3. Let ifx <1 g(x) = x-3 ifx >2 Evaluate each of the following, if it exists. (10 points) lim g(x) lim gx)(i) lim...
(8) Let E c R" and G C Rm be open. Suppose that f E -G and g:GR', so that h -gof:E R'. Prove that if f is differentiable at a point x E E and if g is differentiable at f(x) є G, then the partial derivatives Dh,(x) exist, for all , SO , . . . , n, and and J-: に1 The subscripts hi, 9i, k denote the coordinates of the functions h, g, f relative to...
Question 4 Exercise 1. Let G be a group such that |G| is even. Show that there exists an EG,17e with x = e. Exercise 2. Let G be a group and H a subgroup of G. Define a set K by K = {z € G war- € H for all a € H}. Show that (i) K <G (ii) H <K Exercise 3. Let S be the set R\ {0,1}. Define functions from S to S by e(z)...
Let U ={a, b, c, d, e, f, g, h, i, j, k}. Let A={d, f, g, h, i, k}. Let B={a, d, f, g, h}. Let C={a, c, f. i, k} Determine (AUC) U ( AB). Choose the correct answer below and, if necessary, fill in the answer box in your choice. OA. (AUC) U(ANB)= } (Use a comma to separate answers as needed.) OB. (A'UC) U (ANB) is the empty set. LE This Question: 1 pt Let U={x|XEN...