HK Lee
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 9 multivariable limit of $\frac{x^2-y^2}{\sqrt{x^2+y^2}}$ 6 Show that $g(a) = g(b) = 0,\ \int_a^b f(x)g(x)dx=0$ implies $f(x)=0$ 6 Compute $\displaystyle \lim_{x \rightarrow -3} \frac{\frac{1}{3} + \frac{1}{x}}{3+x}$ 6 Is the set of rationals between $\sqrt{2}$ and $\sqrt{3}$ open or closed in $\mathbb Q$? 6 Exponent of matrix

### Reputation (4,581)

 +15 Positive definite matrix proof with post +15 Let $1 \leq p <\infty$ and $f \in L^p(\mathbb{R})$. Prove $\lim_{x \to \infty} \int_x^{x+1} f(t) dt = 0$. -2 Property of Subadditive function on $L^p(X)$. +15 Orthonormal frame on hyperbolic plane

### Questions (147)

 9 Is $\mathbb Z _p^*=\{ 1, 2, 3, … , p-1 \}$ a cyclic group? 7 Kunneth formula on product of spheres 7 Triangle with $\sin^2 A +\sin^2 B =\sin C$ 6 Cup product on torus 4 Lie algebra isomorphism between ${\rm sl}(2,{\bf C})$ and ${\bf C}^3$

### Tags (144)

 40 linear-algebra × 36 24 multivariable-calculus × 21 34 limits × 16 17 general-topology × 7 33 calculus × 36 12 riemannian-geometry × 39 31 differential-geometry × 60 11 sequences-and-series × 10 27 real-analysis × 34 11 proof-strategy × 6

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