I need to find an equation that is NOT piecewise such that
f(0)=0,
the limit of f(x) as x approaches 0 from the positive side = 1/2,
and the limit of f(x) as x approaches 0 from the negative side = -1/2.
Are there any equations in which a jump discontinuity naturally occurs?
2026-03-25 16:20:34.1774455634
Nonpiecewise Jump Discontinuity
91 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in LIMITS
- How to prove $\lim_{n \rightarrow\infty} e^{-n}\sum_{k=0}^{n}\frac{n^k}{k!} = \frac{1}{2}$?
- limit points at infinity
- Calculating the radius of convergence for $\sum _{n=1}^{\infty}\frac{\left(\sqrt{ n^2+n}-\sqrt{n^2+1}\right)^n}{n^2}z^n$
- Maximal interval of existence of the IVP
- Divergence of power series at the edge
- Compute $\lim_{x\to 1^+} \lim_{n\to\infty}\frac{\ln(n!)}{n^x} $
- why can we expand an expandable function for infinite?
- Infinite surds on a number
- Show that f(x) = 2a + 3b is continuous where a and b are constants
- If $a_{1}>2$and $a_{n+1}=a_{n}^{2}-2$ then Find $\sum_{n=1}^{\infty}$ $\frac{1}{a_{1}a_{2}......a_{n}}$
Related Questions in CONTINUITY
- Continuity, preimage of an open set of $\mathbb R^2$
- Define in which points function is continuous
- Continuity of composite functions.
- How are these definitions of continuous relations equivalent?
- Show that f(x) = 2a + 3b is continuous where a and b are constants
- continuous surjective function from $n$-sphere to unit interval
- Two Applications of Schwarz Inequality
- Show that $f$ with $f(\overline{x})=0$ is continuous for every $\overline{x}\in[0,1]$.
- Prove $f(x,y)$ is continuous or not continuous.
- proving continuity claims
Related Questions in PIECEWISE-CONTINUITY
- Continuity of composite functions.
- Multivariable piecewise function optimization
- Find $k$ so that the following function is constant on any interval
- Piecewise functions in MATLAB. Help!
- Piecewise functions "overlap"
- To check whether the function is piecewise continuous or not
- Is function $f(x) = \frac{x^{2}-2}{x-\sqrt{2}}$ continuous for all $x$?
- How does Raph Levien's Spiro choose angles for the ends of a path?
- Let $x_1,x_2,...,x_n$ be n points in $\mathbb{R}^m$. Is the function $F(w)=max(w^Tx_1,w^Tx_2,...,w^Tx_n)$ differentiable for all $w$?
- Find all $x\in\mathbb R$ that satisfy the equation $|x| − |x − 1| = 1/2$ . Sketch the graph of the equation $y = |x| − |x − 1|$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
How about $\frac{1}{2} \left( \left\lfloor \frac{x}{|x|+1} \right\rfloor - \left\lfloor \frac{-x}{|-x|+1} \right\rfloor \right)$? (Stolen shamelessly from the obvious Wikipedia page.), where $\lfloor \cdot \rfloor$ is notation for the floor function.