1. Define the function sgn by: ifx>0 ifx=0 sgn(x) = 0 Now define h(x): [0,1]R by 51 if0cz ifx=0 h(z) =(sgn(sin(1/4)) i Prove that h(x) is integrable.
) ) (define counter (new-count)) (define foo (lambda (x) (+ x (- 0 x) x)) ) (display (foo (counter))) 1 0 N (display (foo (counter) ) ) 1 0 2 -1 Question 13 (1 point) What would be output of the following code, assuming that normal order evaluation is used? (You may assume all arguments are evaluated left to right.) (define new-count (lambda () (let ((cnt 0)) (lambda () (set! cnt (+ 1 cnt)) cnt ) ) ) (define counter...
(2) Define the set AC by A -{int el: n-0 (d) Prove that A is compact. (2) Define the set AC by A -{int el: n-0 (d) Prove that A is compact.
Define x1 (t) = cos(Ft) for allt € R. Define 0<t<1 Compute (11 * x2)(t), showing all your workings. 0 otherwise. 1 C ={ :
What are some of the benefits of licensure, certification, and registration for health information management (HIM) professionals? What are some of the benefits to the public? Define each of the terms above: licensure, certification, and registration. Then, link them with biblical passages that can support the definitions and how they are used within the field. Being a credentialed professional reflects one’s training, competence, and fitness to provide HIM services. Defend why being credentialed is important both ethically and biblically. Incorporate...
. For > 0 and A > 0, define the joint pdf -Ay = 0<x<A,<y, fx.y(,y) 10 else. (a) Express c in terms of X and A. (b) Find E[XY]. (c) Let [2] be the largest integer less than or equal to z. For example, (3.2] = 3 and [2] = 2. Find the probability that [Y] is even, given that 4 <x< 34
(h) Define f : [0, 2] + R by 122 if 0 <<<1 f(x) = { ifl<152 Using the limit definition of the derivative and the sequence definition of the limit prove that f'(1) does not exist.
10. Define the complex-valued function of a complex variable f:C- Cby 0, z-0 Show that the Cauchy-Riemann equations hold at z 0 but that f is not differentiable at z 0.
Define A E R3x3 as / 2 0 0 A = | 1 2 1 1-1 0 1 ) Calculate p(A) where p(1) = (1 - 2)2(1 – 1). Hint: It will be much simpler to calculate this if you use that p(A) = S-1p(D)S. --(1 : )
let a > 0 and define g(x) := x^(a+1) - (a+1)x + a. Use the mean value theorem to show that g(x)>0 for all x>0, where x~=1 3. Let α > 0 and define g(x):-Χα +1-(α + 1)x + α. Use the mean value theorem to show that (x>for allx >0, where x I 3. Let α > 0 and define g(x):-Χα +1-(α + 1)x + α. Use the mean value theorem to show that (x>for allx >0, where x...