Question

In: Advanced Math

We will say that function f(x) is Lipschitz continue on closerd intervsl [a,b] if exists constant...

We will say that function f(x) is Lipschitz continue on closerd intervsl [a,b] if exists constant K > 0 such yhst | f(x) - f(y) | < or equal to K|x-y|. prove that function f(x) is lipschitz continue then it is uniformly continue.

Solutions

Expert Solution


Related Solutions

Exercise We say that |A| = |B| if there exists a bijection f : A →...
Exercise We say that |A| = |B| if there exists a bijection f : A → B. (a) Show that the intervals [1, 2] and [3, 7] have the same cardinality. (b) Show that the intervals (0, 1) and (0, ∞) have the same cardinality. (Hint: First try (0, 1) and (1, ∞) (later subtract 1). Identify numbers small numbers in (0, 1) with large numbers in (1, ∞) somehow.) (c) Show that the interval (0, 1) and the real...
Say we have a continuous random variable X with density function f(x)=c(1+x3) (where c is a...
Say we have a continuous random variable X with density function f(x)=c(1+x3) (where c is a constant)with support SX =[0,3]. a.) What value of c will make f(x) a valid probability density function. b. )What is the probability that X=2? What is the probability that X is greater than 2? Now say we have an infinite sequence of independent random variables Xi (that is to say X1, X2, X3, ....) with density f(x) stated earlier. c. What is the probability...
consider the function f(x) = 1 + x3  e-.3x a. what is f'(x) b. what is f''(x)...
consider the function f(x) = 1 + x3  e-.3x a. what is f'(x) b. what is f''(x) c. what are the critical points of f(x) d. are the critical points a local min or local max or neither? e. find the inflection points f. if we define f(x) to have the domain of [2,50] compute the global extreme of f(x) on that interval
If a function f(x) is odd about a point, say (a,0), on the x-axis what exactly...
If a function f(x) is odd about a point, say (a,0), on the x-axis what exactly does this mean? How would you relate f(x values to left of a) to f(x values to right of a)? Similarly, if a function f(x) is even about a point, say (a,0), on the x-axis what exactly does this mean? How would you relate f(x values to left of a) to f(x values to right of a)? I understand what is meant by odd...
A function is odd function if f (-x) = - f(x). A function is even function...
A function is odd function if f (-x) = - f(x). A function is even function if f(-x) = f(x). f(x) = sin (x) and f(x) = x are examples of odd functions and f(x) = cos x and f(x) = e^ (-x)^2 are examples of even functions. Give two more examples of even functions and two more examples of odd functions. Show that for odd functions f (x), integral of f(x) from negative infinity to infinity = 0 if...
Function   f (x) = a x + b     for IxI < 2 = 0 for x others...
Function   f (x) = a x + b     for IxI < 2 = 0 for x others    Determinate Fourier series from n= 0 until n= 2
a) State the definition that a function f(x) is continuous at x = a. b) Let...
a) State the definition that a function f(x) is continuous at x = a. b) Let f(x) = ax^2 + b if 0 < x ≤ 2 18/x+1 if x > 2 If f(1) = 3, determine the values of a and b for which f(x) is continuous for all x > 0.
Rolle's Theorem Question if f(a)=f(b) then it is constant function, so every point c in the...
Rolle's Theorem Question if f(a)=f(b) then it is constant function, so every point c in the interval (a,b) is zero. I don't understand the terms constant function, is it supposed to be a horizontal line or it can be a parabola curve. For example, when f(a)=f(b) and they both exist at the endpoint then it can be a parabola curve then it break the assumption that f(a)=f(b) then it is constant function, so every point c in the interval (a,b)...
1. If we have to f(x) = x^5, then: a. determine the equation of the function...
1. If we have to f(x) = x^5, then: a. determine the equation of the function g(x), which takes f(x), stretches it vertically by a factor of 3, then reflects it horizontally, and then moves it 2 units up. b. Graph g(x)
We’ll say a polynomial f(x) ∈ R[x] is prime if the ideal (f(x)) ⊂ R[x] is...
We’ll say a polynomial f(x) ∈ R[x] is prime if the ideal (f(x)) ⊂ R[x] is prime. If F is a field with finitely many elements (e.g., Z/pZ), prove that f(x) ∈F [x] is prime if and only if it’s irreducible.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT