This
is such an example as required.I hope the answer will help
you.Expecting a thumbs up if you are satisfied with the work,it
will help me a lot.Thank you.
© Give an example of sets A and B and a con- Jinuous function f. Au...
R such that f is integrable on every [a,b] (6) Suppose f is a function and a where b> a. Then we define the improper integral eb f(x)dx=lim | b-oo Ja f(x)da, if that limit exists. Assume that f(x) is continuous and monotonically decreasing on [0,00). Prove that Joof exists if and only if Σ f(n) converges. This result is known as the integral test for series convergence.
PROVE:
4. If f : R → R is a strictly increasing function, f(0) = 0, a > 0 and b > 0, then
3. Let f : (a,b) +R be a function such that for all x, y € (a, b) and all t € (0.1) we have (tx + (1 - t)y)<tf(x) + (1 - t)f(y). Prove that f is continuous on (a,b).
(b) ONLY! Though you can use the result from (a) without
proof
(a) Let F(x) = x + x2 + x3 +... and let G(x) = x - x2 + x3 – x4.... Show that for k > 1 and n>k, (4")F(x)* = (n = 1) and if n < k then [x"]F(x)k = 0. (b) Show that G(F(x)) = x.
2. For the difference cquation, X2+] = ax, + b = f(x,), where 0 <a < 1 and b> 0, use the solution given in (1.12) to find the following limit: lim ->XX7. Show that this limit is also a fixed point of the difference cquation, that is, it is a solution x of t = f(x) (see Figure 1.2).
Suppose that f is integrable on (a, b) and define (f(x) if f(x) > 0 f+(x) = 3 and f (2)= if f(x) < 0, Show that f+ and f- are integrable on (a, b), and If(x) if f(x) > 0, if f(x) < 0. cb Sisleyde = [* p*(e) ds + [°r(a)di. | f(x) dx = | f+(x) dx + 1 f (x) dx.
Problem 2 If the cumulative distribution function of X is given by o F(b) = b<0 0<b<1 1<b<2 2<b<3 3<b<3.5 b> 3.5 1 calculate the probability mass function of X.
Please Answer 135 Below Completely:
Definition Let E-R and f : E-+ R be a function. For some p E E' we say that f is continuous at p if for any ε > 0, there exists a δ > 0 (which depends on ε) such that for any x E E with |x-Pl < δ we have If(x) -f(p)le KE. This is often called the rigorous δ-ε definition of continuity. A couple of things to note about this definition....
Let the universal set be R, the set of all real numbers, and let A {xE R I -3 sxs 0, B {xER -1< x 2}, and C xE R | 5<xs 7}. Find each of the following: (a) AUB {xR-3 < x2} s -3orx > 과 xs. (b) AnB xR-12 {*E찌-1 <xs마 frER< -1 orx {*ER|x s -1 or*> 아 (c) A {*ER-3 <x< 아} {*ER|-3 < 아} s-3 orx> 아 frER< 3 orx x s 0 (d) AUC...
Bridging Problem: One Collision After Another © 27 of 27 > Review | Constants Choose the target variables of the problem. Check all that apply. ► View Available Hint(s) mc: mass of sphere C C) velocity of sphere Cafter the second collision Sphere A, of mass 0.600 kg, is initially moving to the right at 4.00 m/s. Sphere B. of mass 1.80 kg, is initially to the right of sphere A and moving to the right at 2.00 m/s. After...