Show that a uniformly continuous function on (a, b) is bounded.

Q: True or false ? I are Continuous on [aib] then f and g

A:

Q: Let xn -> 0 and (yn) be bounded. Prove xnyn -> 0.

A: A sequence is bounded if it is bounded above and below, that is to say, if there is a number, k,…

Q: Prove that f(z)= 1/(1-z) in not uniformly continuous for |z|

A:

Q: Show

A:

Q: Show that the following functions are continuous on their naturaldomains.

A:

Q: Theorem : Let f be defined on [a, b] , if f has a local minimum at a point x € (a, b), and if f'(x)…

A:

Q: Prove that a decreasing function f on [a,b]is integrable.

A:

Q: B) Let f:[-2,2] R, then show that the function sin for x 0, f(x) = 0) for x 0, is uniformly…

A:

Q: ɔ that h is a continuous functi (x2 — 2, х < 6 h(x) 3= 7х + a, х 6

A:

Q: Suppose  f is a continuous function defined on a closedinterval [a, b].(a) What theorem guarantees…

A: [a,b] is a closed and bounded interval. And f(x) is a continuous function.  So by the Extreme value…

Q: Prove that the function f(x) = 2x is uniformly continuous on R.

A:

Q: Let f : E → R be uniformly continuous. Prove that |f| is uniformly continuous. Is the converse true,…

A: Let f: E → R be uniformly continuous.  Now, we need to show that |f| is uniformly continuous.  Now,…

Q: Show that f(x) = 1 x is not uniformly continuous on (0,1) but it is uniformly continuous on [1,2]

A: The function is continuous at x=a if, lim(x→a+)= lim(x→a-)=f(a)

Q: Let f:X→R be a Lipschitz continuous function defined on X. Show that f is uniformly continuous on X.

A: Given : function f:X -&gt; R is a Lipschitz continuous function defined on X . To show : f is…

Q: A function that is uniformly continuous on a set S is not necessarily continuous on S.

A: Given statement A function that is uniformly continews on a set S is not necessarily continews on S…

Q: Is f(x) = x² uniformly continuous on (0,1)? Why or why not?

A:

Q: B) Let f:[-2,2]R. then show that the function xsin -) for x 0, f(x) = for x = 0, is uniformly…

A:

Q: 4. Prove fx=x2+4 is not uniformly continuous on R

A:

Q: 8. Prove that a function which is uniformly continuous on X is also continuous on X

A:

Q: If (a) is decreasing and bounded below, then it is divergent. ylgn ihi

A: False

Q: Let X,X2,.X, be uniformly distributed on the interval (0, a). Find the moment estimator of a.

A: To find the moment estimator of a, we equate the sample moment to population moment.

Q: Let f be a function defined on R satisfying If(z) - f(y)| < 히 - J), V,yER. a. Show that f is a…

A: Given that f be a function defined on ℝ satisfying…

Q: Prove that if f is continuous on [a, b] and F(x) = ſx ƒ (t)dt α then F is continuously…

A:

Q: A bounded function f which has only a finite number of points of discontinuity in [a,b] is…

A:

Q: (b) Determine whether A (2, 9) + (0, 0) (r,y) = (0,0) f(r, y) = %3D continuous or not.

A:

Q: Suppose that fn ⇒ f on R and that each fn is a bounded function. Prove that f is bounded.

A: Solution

Q: Show that the function f(x) = is uniformly continuous on [10, 20] but not uniformly continuous on…

A:

Q: a) Show that, any function f: X → Y is continuous if X have discrete topology.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Prove that if f is a real-valued continuous function on [a, b] × [c, d], then f takes on a maximum…

A:

Q: Show (in terms of  −δ) that a function f : [2,7] −→R be defined by f(x) = √x2+1 is uniformly…

A:

Q: If f is continuous on (a, b), then f attains an absolute maximum value f(c) and an absolute minimum…

A:

Q: Prove the following result: A function f that is decreasing on [a,b] is integrable on [a,b].

A: Prove the result that,        "A function f that is decreasing on[a,b] is integrable on[a,b]''

Q: Suppose that ƒ is a Riemann integrable function on [a, b]. Prove, in two lines only, that if f is…

A: Bounded function

Q: Suppose f is uniformly continuous on [n, n + 1] ∀ n ∈ N. Does it follow that f is uniformly…

A:

Q: ® let f:X→R Cunt f X is bounded $ clused then f is uniformly conto

A: We have to prove that f is uniformly continuous if f is continuous, bounded and closed.

Q: Prove that f : [−4,2] → R defined by f(x) = 7/x+5 is uniformly continuous on the interval [−4, 2]…

A:

Q: 1. Show (in terms of -5) that a function f: [2, 7] R be defined by f(r) V+1 is uniformly continuous.

A:

Q: Let f: X→Y, g:Y-Z be uniformly continuous. Then gof:X-Z is uniformly continuous.

A: The main objective is to proof that the function g∘f is uniformly continuous, i.e. for every ε&gt;0,…

Q: Let f : [0,∞) → R. Assume that f is uniformly continuous on [0, 1] and on [1,∞). Show that it is…

A:

Q: All continuous functions are integrable. A True B False

A:

Q: Suppose that f and g are integrable. Show that f *g is also integrable.

A:

Q: Every continuous function on R satisfies the conditions of MVT. * False True

A: We have to evaluate that the statement, ''Every continuous function on R satisfy the conditions of…

Q: If f : R + Ris continuous and periodic, prove that f is uniformly continuous.

A: Given f:R→R is a periodic function with period k that is f(x+k)=f(x) To prove: if f:R→R is…

Q: Give an example of a bounded function that is defined on R, continuous at each point except the…

A: here i am using both upper and lower limit at x=1,-1 are different and value at these point are also…

Q: Exercise#5 uniformly continuous on I. Is the converse true? Justify. Prove that if the function f: I…

A:

Q: Use theorem 5.2 to prove directly that the function f(x) = x* is integrable [0, 1]. on

A: Using the given Theorem 5.2 we have to prove directly that the function fx=x3 is integrable on [0,…

Q: Show that f(x) = 1/x2 is uniformly continuous on the set [1,∞) but not on the set (0, 1].

A: To show that f(x)=1x2 is uniformly continuous on the set [1,∞) but not on (0,1].

Q: give an example where f is not derivable at [0, ∞), but is uniformly continuous

A: give an example where f is not derivable at [0, ∞), but is uniformly continuous

Q: (5) Suppose that fis continuous on [a, b]- f(x) ≥ 0 Vx = [a,b] and [f(x)dx = 0. Prove that f(x) = 0…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.