Can a curve cross infinitely many times its asymptote?
If so, is there a special name for this behaviour?
2026-03-28 14:55:21.1774709721
Can a curve cross its asymptote infinitely many times?
241 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in PLANE-CURVES
- Finding a quartic with some prescribed multiplicities
- How to use homogeneous coordinates and the projective plane to study the intersection of two lines
- Suggest parametric equations for a given curve
- Interpolation method that gives the least arc lenght of the curve.
- Tangent plane when gradient is zero
- Show this curve is a closed set in $R^2$ by using the definition
- Let $F(X,Y,Z)=5X^2+3Y^2+8Z^2+6(YZ+ZX+XY)$. Find $(a,b,c) \in \mathbb{Z}^3$ not all divisible by $13$, such that $F(a,b,c)\equiv 0 \pmod{13^2}$.
- Find the equation of the plane which bisects the pair of planes $2x-3y+6z+2=0$ and $2x+y-2z=4$ at acute angles.
- Could anyone suggest me some good references on interpolation that include other mathematical structures than just single variable functions?
- Question on the span of a tangent plane
Related Questions in CURVES
- Studying regular space curves when restricted to two differentiable functions
- The problem in my proof that if $\beta(s)=\alpha(-s)$ then the torsions of the curves satisfies $\tau_{\beta}(s)=-\tau_{\alpha}(-s)$
- Given a circle, can i assume that the point where all the normals went thought and the point where all the tangents are equidistants are the same?
- Function determining temperature of points along a curve (find local maxima temp & local minima temp)
- Reference for $L$-functions of curves
- About the Green's Theorem
- inhomogeneous coordinates to homogeneous coordinates
- Can the relocation of one control point of a NURBS curve be compensated by an adjustment of some weights?
- $\| \gamma'(t) \|$ = constant for all $t$, if and only if $\gamma''(t)$ is normal to the tangent vector space for all $t$.
- proving that a curve with constant curvature contained in a sphere its a circle
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?
Quoting from wikipedia, this is the definition of asymptote.
In analytic geometry, an asymptote (/ˈæsɪmptoʊt/) of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity
Consider the curve $ \frac{\sin x}{x} $. It's asymptote simply is $ x = 0 $, yet the asymptote does cross the curve infinitely many times.
I am not aware of a special name for this behavior.