# math_man

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 6 Evaluating $\lim_{x\to0}\frac{1-\cos(x)}{x}$ 4 Question about the limit $\lim_{x\rightarrow 0}{\sqrt{2+\arctan(1/x)}}$ 4 How to solve this limits question 3 Connected set on topology - Contradiction 3 Explain this consequence of continuity

# 1,325 Reputation

 +10 Show that $4\frac{\partial}{\partial z}\frac{\partial}{\partial\bar{z}}=\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}$ +10 Prove rigorously: $\displaystyle \lim_{x\rightarrow 2}x^2+5x=14$ +10 Proving $\lim \limits_{n\to +\infty } \left(1+\frac{x}{n}\right)^n=\text{e}^x$. +2 Errata in Algebra Demystified book?

# 4 Questions

 3 Egorov's Theorem for $\mathbb{R}^n$ 1 Covariant differential on p forms 1 Suppose $u \in C^2(\Omega)\cap C^1(\bar\Omega)$ satisfies $-\Delta u+u^3=0$ in $\Omega$ 1 Some Help to prove $\|T^{-1}\|=\|T\|^{-1}$

# 52 Tags

 31 calculus × 18 6 exponential-function × 2 25 limits × 11 5 continuity × 4 9 real-analysis × 11 5 differential-equations × 4 8 derivatives × 6 4 algebra-precalculus × 3 7 multivariable-calculus × 5 4 analysis × 2

# 2 Accounts

 Mathematics 1,325 rep 2415 MathOverflow 101 rep