Purchase Solution

Discontinuity property of all values

Not what you're looking for?

Ask Custom Question

Please show all work.

Problem 1:

Prove that if f is continuous at all values of x then so is kf where k is a constant.

Problem 2:

Give an example of a function that is continuous at all non-integer values but is discontinuous at all integer values. Prove the discontinuity property of your function (i.e. that it is discontinuous at all integer values).

Purchase this Solution
Solution Summary

In this solution, we illustrate the discontinuity property of the given values.

Solution Preview

Dear Student
** Please find the attachment for the complete solution response **

Problem 1:

Prove that if f is continuous at all values of x then so is kf where k is a constant.
Given that f is continuous at all values of x.
If 'a' is in the domain of the function f, then f is continuous at x=a
This means that for every given (please see the attached file) however small it may be, there exists such that (please see the attached ...

Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Probability Quiz

Some questions on probability

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

View More Free Quizzes
Related BrainMass Solutions

  • Finding the domain and range of discontinuous functions

    Domain Definition Domain is the set of all real values that the independent variable "x" can assume. The domain of the function is set of all possible input values.

  • Fourier transform of both discrete and continous signals

    It is called Gibbs phenomenon, which is caused by the discontinuity in sinc(t) at t = 0, and we tried to use summation of a series of continuous function periodic sine(f) in the Fourier series to simulate the sharp discontinuity.

  • Continuity, Trends and Forecasting

    From mathworld.com the definition of continuous is: A general mathematical property obeyed by mathematical objects in which all elements are within a neighborhood of nearby points. The continuous maps between topological spaces form a category.

  • Dirichlet's theorem on both types of discontinuity

    432107 Dirichlet's theorem on both types of discontinuity Please see the attached file. a) Sketch the periodic function y=ex, ‐2< x <2 and y(x)=y(x+4) for values of x from ‐6 to 6.

  • Fourier series

    points of discontinuity due to the Gibbs phenomenon.

  • Real Analysis : Jump Discontinuity

    This is the jump discontinuity. Thus the only type of discontinuity of a monotone function can have a jump discontinuity. Jump Discontinuities are investigated. The solution is concise.

  • Removable discontinuity, jump and essential discontinuities.

    This solution is comprised of a detailed explanation for removable discontinuity, jump discontinuity and essential discontinuity.

  • Gibbs Phenomenon and Fourier Series expansion

    Your goal is to answer these two questions: (a) You should find that the amount of overshoot only depends on the height of the discontinuity of your function.

  • Discontinuous function

    In this chapter, all the functions we meet will be continuous at every point except in one of the three cases discussed below. This shows how to determine if functions are discontinuous and solves a problem using jump discontinuity.

View More Related Solutions