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5. Let f(x)- arctan(x) (a) (3 marks) Find the Taylor series about a 0 for f(x). Hint: - arctan(x) - dx You may assume that the Taylor series for f(x) converges to f (x) for values of x in the interval of convergence (b) (3 marks) What is the radius of convergence of the Taylor series for f(x)? Show that the Taylor series converges at x-1. (c) (3 marks) Hence, write T as a series (d) (3 marks) Go to...
Let U ~uniform(0,1). Let Y =−ln(1−U). hint: If FX (x) = FY (y) and supports x,y ∈ D, X and Y have the same distribution. Find FY (y) and fY (y). Now, it should be straight forward that Y follows distribution with parameter_____________-
Integration By Parts: Evaluate the integral. Hint: Use ſuav=UV- (v.au 1 x Inx dx 1+ln(2) In(2) O2 21n(2)
Please answer and state letter choice, will upvote | arcsin(ln(I)) dx = In(2) a) ln(2) arcsin (In(2)) - V1 - (In(x))24 b) In (2) arcsin(In(2) . ln(2) TavI - (In(z)2 de c) O ln(x) arcsin(ln(n)) - ) Tv I – (In(z)2 47 a) O arcsin (In(a) – | In(z) _ *V1 - (ln(x)}2 dr e) arcsin In(1) V1 - (In(x)) O + ("anef ; (eorge Hoc @foܘܨ(f + ( P ܘܢ ,") +o ) ioo + ܕܡܨ(o ' t »nfoܨ,")...
5-1. Let U ~ Uniform(0,1) and X = – ln(1 – U). Show that The CDF of X is Fx(x) = 1 – e-X, 0 < x < 0 In other word, X is exponentially distributed with 2 = 1.
let u= ln(x) and v=ln(y) w=ln(z) where x,y,z>0 .Write thr following wxpressiins in terms of u,v, and w. a) ln( squareroot x^5)/ y^3z^2) B) ln (squareroot x^3 4squaroot y)
SP: Aşağıdaki integrallerini hesaplayınız. z arctan(x)dx a) ſta b) [ 1 (1+x2) -da
1 (a) Consider the integral dx. e32 e-91 + e-6x +1 Make the substitution u = e-34 and rewrite the integral in terms of u only. DO NOT attempt to evaluate the integral. (b) Let f(x) be a function with the properties that f(0) = 1, f(2) = 2, xf(x) dx = 4 and f(x) dx = 1. / 0 Use this information to find a se xf'(2) dr.
5. a. By completing the sequence, show that 2 TC dx x2 - x + 1 = 3V3 Hint: d arctan x = dx 1 x2 + 1 b. Show that 3V3 T = (-1)" on
Question 1 12 Evaluate: So x2 arctan(x) dx = HTML Editor B I y A - A - IX EE 3 7 2 xx, 5 E * CV TT: 12pt