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 Find the limit of $\lim \limits_{x \to 1} \frac{\sqrt[\leftroot{0}\uproot{2}3]{5x-4} - 1}{\sqrt[\leftroot{0}\uproot{2}4]{5x-4} - 1}$

### Reputation (2,120)

 +5 Why is $(e_n)$ not a basis for $\ell_\infty$? +55 Find the limit of $\lim \limits_{x \to 1} \frac{\sqrt[\leftroot{0}\uproot{2}3]{5x-4} - 1}{\sqrt[\leftroot{0}\uproot{2}4]{5x-4} - 1}$ +35 Compute $\oint_{|z|=r}z^2 \sin(\bar z)dz$ +10 Verify that $\sqrt{2}\left\| z \right\| \ge \left|\Re(z)\right| + \left|\Im(z)\right|$

### 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 Why is $(e_n)$ not a basis for $\ell_\infty$? 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

### Tags (75)

 32 calculus × 27 12 multivariable-calculus × 7 26 limits × 24 12 complex-analysis × 4 24 sequences-and-series × 17 11 ordinary-differential-equations × 12 22 integration × 19 9 laurent-series × 2 16 indefinite-integrals × 7 8 real-analysis × 8