Q1 (4 points) Assume that f: NXN N is a function defined by f(n, k) =...
Q1 (5 points) Does the sequence a n converge or diverge? If it converges, find its limit. + Drag and drop your images or click to browse
Q3 (3 points) Show that if both AB and B A are defined then AB and BA are square matrices. + Drag and drop your images or click to browse... Q4 (3 points) Let A = (a) be a 2 x 2 matrix. The trace of A. which we denote by tr(A) is a number defined as tr(A) = 0 + 0x2. Prove the following properties of this number for 2 x 2 matrices A and B and a real...
Please answer all parts with full, clear solutions so i can understand :) :) Q2 (6 points) If C is a smooth plane curve with parametrization r r(t),t E [a, b], then the curvature K(t) of C at the point r(t) is defined to be the magnitude of the rate of change -ll dT of the unit tangent vector with respect to the arc length. That is, = ds () [2p] Show that K(t) = ||F (C) xr" (t)|| r...
Please explain you're answers step by step and make sure you're answer is correct! Q1 (10 points) X and Y are random variables with ƠX-7, ơY-1 and coefficient of correlation PXY =-0.1 . Calculate the standard deviation of Drag and drop your images or click to browse.
Q1 (10 points) We want to compute the volume when we revolve a region about an axis using the disk method. The region we are interested in is bounded by y = x, y = 0, x = 2. Provide a sketch of the region clearly labeling the intersection points. + Drag and drop your files or click to browse.... Q2 (10 points) We want to revolve this region about the z-axis. On the sketch of the region, clearly label...
Assume that V is the set of all complex sequences, (xn), that satisfy the relation Xn+nXn+1 – ixn+4 = 0 for all n E N. Furthermore, assume that F = C and for a E C, (2n), (yn) € V define (xn) + (yn) = (xn + yn), a(xn) = (axn) Is V a vector space over C? Justify your answer.
For each function defined below, find the value of k such that s(n) = O(n). For part (a), justify your answer from the definitions of 0, 0, and 2 by finding explicit constants that work For part (b), you do not need to find explicit constants, just explain why your answer is correct. (a) s(n) = (2n + 1)(5n² +1) (b) s(n) = nºt(n) + no where t(n) = O(n") (Hint: answer in terms of b.)
Answer the questions in the space provided below. 1. The definition of a function f: X + Y is as a certain subset of the product X x Y. Let f: N + N be the function defined by the equation f(n) = n2. For each pair (x, y) listed below, determine whether or not (x,y) ef. a) (2,4) b) (5, 23) c) (1,1) d) (-3,9) 2. For each function defined below, state whether it is injective (one-to-one) and whether...
Consider the function f : {0,1} » N → NU{0} defined as f(x,y) = (-1)22 y. Is f injective? Surjective? Explain your answer.
2. Show that the function f:N→Q defined by f(n) = is injective but not surjective.