Solution
2. Show thatf-dr= nn (Hint: First write a n-n (Hint: First Your answer to 0 problem 1 will be useful 2. Show thatf-dr= nn (Hint: First write a n-n (Hint: First Your answer to 0 problem 1 will be...
(a) Show that for > 0, the first integral equals: 0 n-0 (b) Show that 1) n=0 defines a continuous function on Ω :-R\{0,-1,-2,-3, . . . } [Hint: consider the domain R\ U000 (-n-e,-n + ε) for any small ε > 0.]
(a) Show that for > 0, the first integral equals: 0 n-0 (b) Show that 1) n=0 defines a continuous function on Ω :-R\{0,-1,-2,-3, . . . } [Hint: consider the domain R\ U000 (-n-e,-n + ε)...
Utilizing the comparison tests, show that if use the information in your conclusion to show that if Hint: you may note that 2 2 2 n 2 4, In(n) < Vn In(n) - In(4)-dr 2 2 2 n 2 4, In(n)
a) Show that the series CO (e n 0 n 0 on the interval 10, co towards the function Converges pointwise 1 t e]0, co[ f(t) 1 — е- b) Show that the series CO пе-nt п3D0 converges uniformly for t in the interval [b, o for every constant b > 0. Let CO ne nt t> 0, s(t) n 1 be the sum function of the series. J0, co[ d) Show thatf'(t) = -s(t) for all t > 0...
2c. (10 pts) Show that f given in 2b) is intergrable and [ 1 (2) dr = 2Ě (2n-1) 2d. (10 pts) Let 0 < < be given. Show that f given in 2b) is differentiable at each 1 € (5,27 - 8). Find f' (1). Hint: Use Problem 1 and the following formula In 2 (-1)"-1 Σ 7 n=1 2. (40 pts) Let fn: R → R be given by fn (x) = sin (nx) 3 ηε Ν. n2...
Problem 2 Show that if the sequence of numbers (an)n-1 satisfies Inlan) < oo, then the series In ancos(nx) converges uniformly on [0, 27). This means, the partial sums Sn(x) = ) ancos(nx) define a sequence of functions {sn} = that converges uniformly on [0, 271]. Hint: First show that the sequence is Cauchy with respect to || · ||00.
Problem 3. Let X be a discrete random variable that takes values in N. Show that if X is memory-free then it must be the case that X Geo(p) for some p. (Hint a useful first step might be to show that P(X > t)= P(X > 1)' for all t E N.)
Problem 3. Let X be a discrete random variable that takes values in N. Show that if X is memory-free then it must be the case that...
Show that the Halting Problem for one-counter additive machines is decidable. Hint: first show that if the machine has n states and the counter reaches zero more than n times in the course of a computation, it will run forever.
Please Prove your answers mathematically, I need clear
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PROBLEM2 y(n) = 2 x(n-2) sin (nn) Determine whether the system Justify your answer and 1. linear 2. time invariant 3. Stahle
Exercise 3 Calculate the area of the entire shape. Include the tolerances and units. Show all your work. Hint: Separating the shape into 2 simpler shapes is useful. Area of a complete circle is tr2 Exercise 2 Using the instrument mentioned in Exercise 1, measure the dimensions of the shape inside the grid below. Write your measurements and tolerances in the spaces provided. /E
Exercise 3 Calculate the area of the entire shape. Include the tolerances and units. Show all...