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seen Mar 13 at 11:28

Jun
23
awarded  Yearling
Mar
3
comment Invertible Matrix and Linearly Independent Vectors Proof
That's right, yes.
Feb
27
answered Invertible Matrix and Linearly Independent Vectors Proof
Feb
26
comment Show that $\lim_{r \rightarrow 1} \sum_{n=1}^{\infty} r^{2^n}= \infty$
... but using your inequality, for each $k\geq 1$, $$\lim_{r\to 1} \sum_{n=1}^\infty r^{2^n}\geq \lim_{r\to 1} kr^{2^k} = k,$$ so the result holds.
Feb
26
comment Show that $\lim_{r \rightarrow 1} \sum_{n=1}^{\infty} r^{2^n}= \infty$
But the condition $r^{2^k}\geq\frac12$ forces $k$ to be small, so we can't say that the sum is larger than something that gets arbitrarily large.
Feb
4
comment Evaluating $\int_\gamma z\big(1+|z|^2\big)^{-1/2}\,|dz|$
You have a small but crucial error here: $|t i e^{it}+e^{it}|=(1+t^2)^{1/2}$. Making this correction will simplify the integral.
Jan
22
comment How to find $\int_{0}^{1}\frac{1}{x^{2}+2x+2}\mathrm dx$ with contour integration
The branch of $\log z$ required has a cut along the positive real axis - is that right?
Nov
2
awarded  Nice Question
Jun
23
awarded  Yearling
Jun
12
comment Show that $x=2\ln(3x-2)$ can be written as $x=\frac{1}{3}(e^{x/2}+2)$
@Lord_Farin - I disagree. This answer provides a useful hint that could allow the asker of the question to work the problem out for him/herself and so learn some maths in the process.
Jun
5
comment How to calculate this integral containing a Dirac delta function
Hint: $$\delta(f(z_0))=\sum_{z_k:f(z_k)=0}\frac{\delta(z_0-z_k)}{|f'(z_k)|}.$$ See this link.
May
30
comment Can any planar graph have 4 vertices and 4 regions?
@Ada - your last comment shows the importance of the definition of 'region' in the question. I think you should clear this up with your professor: he/she may be using a different definition to the one in Grimaldi et al. - or as you suggested originally, there may be a flaw in the question.
May
30
comment Can any planar graph have 4 vertices and 4 regions?
... so as you can see from the planar graph wikipedia page and from the wordpress source you've linked to, $K_4$ has only three regions (i.e. three areas that are enclosed by edges of the graph).
May
30
comment Can any planar graph have 4 vertices and 4 regions?
I wonder is the version of $K_4$ you are thinking of the non-planar representation? See here and then here by way of contrast.
May
10
awarded  Caucus
Apr
17
answered Shortest Vector for which Dot Product = x + 2y = 5. (Strang P21 1.2.26)
Mar
25
comment Complex Numbers Proof
Typo in your second line. $|z|^2$ should be $|z|^2|w|^2$. Things should work out after that.
Mar
25
answered Prove that $|PC|^2 + |PD|^2 = |AB|^2$ if
Mar
21
comment Radius of Convergence for$S=\sum^{\infty}_{0}\frac{2^n(x-2)^n}{(n+2)!}$
You need to take the limit $n\to\infty$ in order to apply the test.
Mar
20
answered Finding nontrivial solutions to a system of equations