user62498

 8 How to compute the residue of $(z^2+2z+1)\sin\left(\frac{1}{1+z}\right)$ 6 Multivariable limit of rational function 5 Integrating $\int \frac {dx}{\sqrt{4x^{2}+1}}$ 5 How would you integrate $\sqrt{1+\frac{1}{x^2}}$ 4 If $x+(4/x)=4$ then $x^3+(4/x)^3$ is

### Reputation (2,025)

 +20 Verify that $\sqrt{2}\left\| z \right\| \ge \left|\Re(z)\right| + \left|\Im(z)\right|$ +5 Book suggestion geometry of Banach spaces +10 Integration method that i forgot. +5 Closed ideal in $L^{1}(G)$

### Questions (81)

 8 The Weak topology on an infinite-dimensional space is not metrizable 6 In a uniformly convex Banach space $x_n\stackrel{w}\to x$ and $||x_n||\to ||x||$ implies $||x_n-x||\to 0$ 5 Riemann integral of $f(x) = \begin{cases} \frac{1}{n}, & \text{if$x=\frac{1}{n}, \ \ n=1, 2,3 ,\cdots$} \\ 0, & \text{other where} \end{cases}$ 5 Exercise books in functional analysis 4 Evaluate $\lim_{n \to \infty} \frac{1}{n}\int_{0}^{n}\frac{x\ln(1+\frac{x}{n})}{1+x}dx$ [duplicate]

### Tags (72)

 32 calculus × 27 12 multivariable-calculus × 7 24 sequences-and-series × 17 11 ordinary-differential-equations × 12 22 limits × 23 10 complex-analysis × 3 22 integration × 19 9 laurent-series × 2 16 indefinite-integrals × 7 8 real-analysis × 8

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