The function is not integrable in [0,1] as the function is discontinuous at each point(infinitely many) in its domain.
Prove that for every positive real (important: is not necessarily an integer), that . Hint: For every , the function is strictly growing. We were unable to transcribe this imageWe were unable to transcribe this imagebe(n") (n log, n) > 0 n
Let n be a positive integer with n > 20 , and let with 1. Show that S possess two disjoint subsets, the sum of whose elements are equal. S 1,2,., 1n2) We were unable to transcribe this image
Give three examples for Rolle's Theorem: For the first, define f : [0, 1] R such that condition 1 does not hold, condition 2 does hold, condition 3 does hold, and f'(c)0 for every c (0,1). For the second example, make sure only condition 2 does not hold and the conclusion do not hold. For the third example, do the same with condition 3. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this...
Given that and given that theta = 0, x = 0, y = mg/k. Find out what x, is 1 0 2 (0) = 0 mg 9(0) 0 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image 1 0 2 (0) = 0 mg 9(0) 0
1. [10 marks] Modular Arithmetic. The Quotient-Remainder theorem states that given any integer n and a positive integer d there exist unique integers q and r such that n = dq + r and 0 r< d. We define the mod function as follows: (, r r>n = qd+r^0<r< d) Vn,d E Z d0 Z n mod d That is, n mod d is the remainder of n after division by d (a) Translate the following statement into predicate logic:...
Find the unique function f(x) satisfying the following conditions: f′(x)=2x f(0)=4 f(x)= We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
1. Find another representation, (r, &theta), for the point under the given conditions. (154),r>0 and 2n<0<47 Select the best answer for the question 2. Find all the complex roots of 144(cos 210° + i sin 210°) in polar form. O A. 12(cos 210° + i sin 210°), 12(cos 195° + i sin 1959) O B. 12(cos 105° + i sin 105°), 195(cos 285° + i sin 285°) O C. 12(cos 105° + i sin 105°), 12(cos 285° + i sin...
Q1) Let X(t) be a zero-mean WSS process with X(t) is input to an LTI system with Let Y(t) be the output. a) Find the mean of Y(t) b) Find the PSD of the output SY(f) c) Find RY(0) ------------------------------------------------------------------------------------------------------------------------- Q2) The random process X(t) is called a white Gaussian noise process if X(t) is a stationary Gaussian random process with zero mean, and flat power spectral density, Let X(t) be a white Gaussian noise process that is input to...
(of I assume) 1 is not a quadratic residue If p 4k3 for some positive integer k, then We were unable to transcribe this image 1 is not a quadratic residue If p 4k3 for some positive integer k, then
Let T : C([0, 1]) → R be a (not necessarily bounded) linear functional. Show that T is positive if and only if = (here 1 denotes the constant function [0, 1] → R, x → 1). We were unable to transcribe this imageWe were unable to transcribe this image