Real Analysis question, give clear writing please
Real Analysis question, give clear writing please Let h(x) be the function on (0, 1) defined...
Real analysis. Please solve all questions thank you 1. Let h be a positive real number, a <c< d < b and let Sh c< x <d, J() = 1 0 r < c, x > d (a) Using the definition only, find ſº f(x)dx. In fact, given e > 0, you should find an explicit d > 0) which works in the definition. (b) For a given partition P of [a, b], find a good upper bound on S(P)...
5. Let be the function defined by f(x) = -1 3 1.5 if r <0 if 0<x<2 if 3 < r <5 Find the Lebesgue integral of f over (-10,10).
Please give clear detailed explanation. Let a 0 and suppose that the function f is Riemann integrable on [0, a]. Prove that f(a-x) dx = 2S0[f(x) + f(a- 1 ca f(x) dx = x)j dx. Prove that f' in(1 + tan(a) tan(x)) dx = a ln(sec(a)) (0<a<T/2) Let f: [0, 1] → R be defined by f(x) = VX , 0 1 , and let x 2 n-1,2 be a partition of [0, 1]. Calculate lRll and show that lim...
Let be a function defined by: We define by extension the odd, periodic function of period p = 2 which coincides with the function f (x) on the interval [0, 1]. Draw over the interval [−1, 3] the graph of the function towards which the Fourier series of the odd continuation of the function f (x) converges. f(x) = 1 + x2 pour 0 < x < 1.
5. Let f,lr)- x *a. Show that {h} converges uniformly to 0 on [0, a] for any a, 0 < a < 1. b. Does {f,) converge uniformly on [0, 1]?
A periodic function f(x) with period 21 is defined by: X + -1<x< 0 2 f(x) = 0<x< 2 Determine the Fourier expansion of the periodic function f(x). X - TT
Previous Answers KaufACS10 8.3.042. 0/1 points| 27. Graph the piecewise-defined function. 1 for x<0 for x >1 4 Actions Tools Clear Al 8 9 1O 1074 32 1 Object Properties Select a Tool or Object to Begin Help graphing tool Submission Data Need Help? Lǐeed IT-ktonteil Subrmit Answer Save Progress Pratice Another Version Practice Another Use the approach of Examples 1 and 2 to graph the quadratic function. esc
9. La ste) defined as follows 9. Let f(x) defined as follows: f(x) = 0 if x < -1 = 2(x + 1)/27 if - 1<x<2 = 2/9 if 2 < x < 5 = 0 otherwise. Find F(u) = f(x)dx, where u E R.
h(y) is function y Question 5 10 pts Let Y = g(x) = x - 1, where the PDF is :1< x < 65 f(x) = { 64 0 : otherwise a) (2 points) Determine h(y) b) (2 points) Determine h' (y) c) (2 points) Determine PDF of y d) (2 points) Determine the CDF of y e) (2 points) What is the P[1 <Y 2] P[ 1 \leq Y \leq 2]
This is the previous question, Pls answer this question, Let f : [0, 1] + R be uniformly continuous, so that for every e > 0, there exists 8 >0 such that |x – y<8\f(x) – f(y)] < € for every x, y = [0, 1]. The graph of f is the set G = {(x, f(x)) : x € 0,1} Show that Gf has measure zero Let f : [0, 1] [0, 1] + R be defined by f(x,y)...