I have a problem with solving following limit. $$\lim_{(x,y)\rightarrow 0}(x^2+y^2)^{x^2y^2}$$ I tried to estimate it let :$$z=max(x^2,y^2)$$ $$z^{z}\le(x^2+y^2)^{x^2y^2}\le (2z)^{z^2}$$ Using 3 function statment i get that limit is 1 where Wolfram shows 0. Will be more than glad for help.
2025-01-12 19:20:31.1736709631
Find function limit
51 Views Asked by vanHohenheim https://math.techqa.club/user/vanhohenheim/detail At
1
There are 1 best solutions below
Related Questions in LIMITS
- Limit of $(5n^2+2n)/(n^2-3)$ using limit definition
- How discontinuous can the limit function be?
- Find function limit
- Using $\epsilon-\delta$ definition to show $\frac{\sqrt{9-x}-3}{x}$ as $x\to 0$
- Name of multidimensional propagator integral
- Clarify books proof limit of $\frac{1}{x}$ diverging at $0$
- Evaluate the following limit using Taylor series.
- Problem with limit of recursive sequence having the actual index "n" in denominator.
- My incorrect approach solving this limit. What am I missing?
- Limit of $f(x)=x-\lfloor x \rfloor$ $\epsilon-\delta$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- 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?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- 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
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity
Hint: Convert to polar coordinates.