For the given function f(x) and numbers L, c, and e > 0, find an open interval about c on which the inequality fx)-L...
Find an open interval about x0 on which the inequality holds. Then give a value forδ>0 such that for all x satisfying the inequality holds:
Consider the function f(x)-e a. Differentiate the Taylor series about 0 of f(x). b. Identify the function represented by the differentiated series c. Give the interval of convergence of the power series for the derivative. a. Choose the correct answer belovw 213 Ос. D. 2 41 61 b. The function represented by the differentiated series is Iill c. The interval of convergence of the power series for the derivative is Simplify your answer. Type an inequality or a compound inequality...
(2) Consider the function f : R → R defined by Í 1 x E [-L,0) f(x + 2L) = f(z) -(x) f( 2L) o E l0,L) a. Graph f on the interval [-3L, 3L]. b. Compute Fi-L,Lf) c. Graph F-L(f) on the interval [-3L,3L] c. Graph Fi-L/2,L/() on the interval [-3L,3L]. (2) Consider the function f : R → R defined by Í 1 x E [-L,0) f(x + 2L) = f(z) -(x) f( 2L) o E l0,L) a....
please check my work if all correct i will give up rating Given fx)> 0 with f"(x) <0, and f"x)> 0 for all x in the interval [0, 2] with f0) - 1 and f2) -0.2, the left, right, trapezoidal, and midpoint rule approximations were used to estimate jfx)dx. The estimates were 0.7811,0.8675, 0.8650, 08632 and 0.9540, and the same number of subintervals were used in each case. Match the rule to its estimate. a. left endpoint b. right endpoint...
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
5. Let fx(x) be a pdf given by fx(x) = (1/8)(e^(-x/8)) for x > 0. a) Find the CDF FX(x). b) Find P(X > 4) c) Find P(-2 ≤ X ≤ 12) d) Find P(X < 240) e) Find E(X) f) Find the standard deviation of X.
[EUM 114 1. Let f(x) be a function of period 2 (a) over the interval 0<x<2 such that f(x) = - f(x)pada selang Diberikan f(x) sebagai fungsi dengan tempoh 2t yang mana 0<x<2m Sketch a graph of f (x) in the interval of 0 <x< 4 (1 marks/markah) Demonstrate that the Fourier Series for f(x) in the interval 0<x< 2n is (ii) 1 2x+-sin 3x + 1 sin x + (6 marks/markah) Determine the half range cosine Fourier series expansion...
Given f(x) = ( c(x + 1) if 1 < x < 3 0 else as a probability function for a continuous random variable; find a. c. b. The moment generating function MX(t). c. Use MX(t) to find the variance and the standard deviation of X.
5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 0 < x < π. (Only sketch over the interval z E [-2π, 2π). (b) (10) Find the Fourier sine series of the function in part (a) 5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 0
Question l: Consider the function f(x) = sin(parcsinx),-1 < x < 1 and p E R (a) Calculate f(0) in terms of p. Simplify your answer completely fX) sin(p arcsinx) f(o) P The function fand its derivatives satisfy the equation where f(x) denotes the rth derivative of f(x) and f (b) Show thatf0(n2p2)f(m)(o) (x) is f(x). (nt2) (nti) (I-x) (nt 2 e 0 (c) For p E R-仕1, ±3), find the MacLaurin Series for f(x), up to and including the...
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