Intereting Posts

Normal bundle of a section of a $\mathbb{P}^1$-bundle
Equivalent definitions of Injective Banach Spaces
probability of A dice with X faces beating B dice with Y faces
Is it correct to say that ($\color{red}{(} \limsup |W_k|/k\color{red}{)} \le 1) \supseteq \limsup \color{red}{(}|W_k|/k \le 1\color{red}{)}$?
Equivalence of Archimedian Fields Properties
Zeroes of a holomorphic function
If $a_1,\ldots,a_n>0$ and $a_1+\cdots+a_n<\frac{1}{2}$, then $(1+a_1)\cdots(1+a_n)<2$.
Iff Interpretation
Can only find 2 of the 4 groups of order 2014?
Lebesgue Integral of a piecewise defined function defined on irrationals and rationals(GATE-2017)
Local Submersion Theorem – Differential Topology of Guillemin and Pollack
Evaluating $\int_{0}^{\pi/3}\ln^2 \left ( \sin x \right )\,dx$
Penguin Brainteaser : 321-avoiding permutations
Intuitive explanation of Cauchy's Integral Formula in Complex Analysis
Modified gambler's ruin problem: quit when going bankruptcy or losing $k$ dollars in all

Most of the books that I have (H.K Dass) say that (or at least that’s what I have understood) for the limit of a multivariable function (say f(x,y) ) to exist the limit along every possible path should exist and be equal. That’s the condition for continuity.But for every solved example they do they just consider the limit along y=mx and y=mx^2 and if the limits in these 2 cases come equal they say the limit exists and is equal to answer that they get when evaluating the limit at the point by moving along the above given curves.But we should evaluate the limit along say y=mx^3 and y=mx^4 and say on. In fact in some questions (in which the degree of denominator is greater) in which they get the limit by just evaluating across the linear and quadratic path doesn’t come the same when we evaluate along cubic path. So how can they be sure by just evaluating along the linear and quadratic path. One should be checking for other paths too.But how far can one go checking all the paths. If I have got the concept wrong then what’s the correct one. An example would be appreciated

- What does it mean to multiply differentials?
- Show that $\lim_{n\rightarrow \infty} \sqrt{c_1^n+c_2^n+\ldots+c_m^n} = \max\{c_1,c_2,\ldots,c_m\}$
- Limit of $\frac{\sin(x+y)}{x+y}$ as $(x,y) \to (0,0)$
- What is the limit of
- Uniformly bounded sequence of holomorphic functions converges uniformly
- Fractional anti-derivatives and derivatives of the logarithm
- What's a concise word for “the expression inside a limit”? Limitand?
- Uniform convergence in a proof of a property of mollifiers in Evans's Partial Differential Equations
- Is there any diffeomorphism from A to B that $f(A)=B$?
- Limits in Double Integration

- Closed form of $ \int_0^{\pi/2}\ln\bigdx$
- Proving Newton's identities
- references for the spectral theorem
- Why is the axiom of choice separated from the other axioms?
- What is the difference between writing f and f(x)?
- Which of these numbers is the biggest
- Nice proof for finite of degree one implies isomorphism?
- What is the difference between an indefinite integral and an antiderivative?
- Terminology re: continuity of discrete $a\sin(t)$
- Steiner triple system with $\lambda \le 1$
- prove that projection is independent of basis
- Math and mental fatigue
- Discussion on even and odd perfect numbers.
- Is the function $e^{-|x|^k}$ analytic on any interval not containing zero?
- Is the unit sphere in $\Bbb R^4$ is path connected?