# Joe

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# 161 Questions

 33 Prove $\int_0^1 \left| \frac{f^{''}(x)}{f(x)} \right| dx \geq4$ 14 The limit of $f_n(x)$ 12 Why did we define the concept of continuity originally, and why it is defined the way it is? 10 The roots of Hermite polynomials are all real? 9 An approximate eigenvalue for $T \in B(X)$.

# 1,937 Reputation

 +5 Integrate $\int_0^\pi e^{-ik\cos\theta}\sin^2{\theta} \, \mathrm{d}\theta$ +5 Lebesgue integrable discontinuity points +5 Prove $\int_0^1 \left| \frac{f^{''}(x)}{f(x)} \right| dx \geq4$ +5 Evaluate $\int\limits_0^{\frac{\pi}{2}} \frac{\sin(2nx)\sin(x)}{\cos(x)}\, dx$

 3 Let $a_{n}$ be a sequence such that $(a_{n})^{2}=ca_{n-1}$ where ($c>0,a_{1}>0$).Prove that $a_n$ converges to $c$. 2 Proof that $\int_1^x \frac{1}{t} dt$ is $\ln(x)$ 1 The convergence of the adjoint operator 1 Prove$\frac{1}{\pi}\int^{\pi}_{-\pi}f(x)\cos 2nx \geq 0$ 0 Can you check my proof on piecewise linear approximations?

# 68 Tags

 3 calculus × 39 1 operator-theory × 6 3 real-analysis × 37 1 convergence × 4 3 sequences-and-series × 3 1 adjoint × 2 2 logarithms 0 complex-analysis × 10 1 functional-analysis × 32 0 matrices × 10

# 3 Accounts

 Mathematics 1,937 rep 1623 Physics 116 rep 2 MathOverflow 101 rep 1