helios321
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2 answers
7 votes
255 views
5 bookmarks
For complex numbers $a,b,c$, explain why $a^{b\cdot c}=(a^b)^c$ is not necessarily true.
1 answers
5 votes
367 views
3 bookmarks
Spivak' Calculus Chapter 7 Problem 19(b) [continuity]
3 answers
5 votes
157 views
2 bookmarks
Evaluate: $\frac{1}{(1+1)!} + \frac{2}{(2+1)!}+...+\frac{n}{(n+1)!}$ using combinatorics.
1 answers
5 votes
2k views
1 bookmarks
Eigenvalues without any calculations
0 answers
4 votes
38 views
What is the geometric significance of differentiable vs continuously differentiable?
3 answers
4 votes
120 views
Proof of Fundamental Theorem of Calculus using big O
2 answers
4 votes
299 views
1 bookmarks
Spivak Calculus $13-33$
1 answers
4 votes
242 views
Spivak's Calculus 8-3(a)
2 answers
3 votes
2k views
2 bookmarks
Finding equation and centre of circle through 3 points using matrices
3 answers
3 votes
70 views
1 bookmarks
If $y=\mathrm{e}^x\big(a\sin x+b\cos x\big)$, then express $y^{(n)}$ in terms of $y$ and $y'$.
4 answers
3 votes
104 views
Prove that for any $a,b\in \mathbb{N}$, $\sqrt{a^2+b}=a+\frac{b}{2a+\frac{b}{2a+...}}$.
1 answers
3 votes
349 views
3 bookmarks
Spivak Chapter 11 Question 39
1 answers
2 votes
146 views
1 bookmarks
Spivak's Calculus 12-10(b) Solution seems incorrect
2 answers
2 votes
142 views
By using primitive roots how does one solve $x^2 \equiv -1 \pmod p$ for $x$, given prime $p$.
2 answers
2 votes
47 views
If $A=\left\{a_{1}, a_{2}, \ldots, a_{p}\right\}$ is complete system of residue then $\sum_{1\leq i < j \leq p}a_ia_j \equiv 0 (\text{mod p})$.
0 answers
2 votes
48 views
Does Stokes Thoerem say extend to closed surfaces in $\mathbb{R}^3$?
0 answers
2 votes
26 views
What are the basic assumptions for a line integral to exist?
1 answers
2 votes
204 views
Find a modulus of continuity for $f(x,y)=\sqrt{1+x^2+2y^2}$.
1 answers
2 votes
91 views
1 bookmarks
Find a modulus of continuity $\delta_{\epsilon,x,y}$ for the continuous function $f(x,y)=\sqrt{1+e^{xy}}$.
1 answers
2 votes
111 views
Limit existence rules
2 answers
2 votes
52 views
Proving vectors are rotations about some axis
1 answers
2 votes
85 views
1 bookmarks
If $f$ is continuous, $f'(c)=0$ and $f''(c)<0$, then $f(x)<f(c)$ for all $x$ in an interval around $c$?
1 answers
2 votes
172 views
What is the difference between a continuous and discontinuous complex function visually?
2 answers
2 votes
1k views
3 bookmarks
Proving that the series $\sum\limits_{n=0}^{\infty} 2^n \sin (\frac{1}{3^nx})$ does not converge uniformly on $(0,\infty)$
2 answers
2 votes
191 views
Prove $f_n(x)=\sqrt{x+\frac{1}{n}}-\sqrt{x}$ converges uniformly on $\mathbb{R}$.
2 answers
2 votes
418 views
Prove that if $f(x)= e^{-1/x^2}\sin{\frac{1}{x}}$ for $x\neq0$ and $f(0)=0$, then $f^{(k)}(0)=0$ for all $k$.
1 answers
2 votes
103 views
Spivak 11 Appendix Question 8 understanding solution
1 answers
1 votes
41 views
Let $z \in \mathbb{C}$, what is the derivative of $\frac{1}{a+|z|} $?
2 answers
1 votes
54 views
Show $\left\{(-1)^{n}+1 / n: n \in \mathbb{N} \setminus \{0\}\right\} \subseteq \mathbb{Q}$ has no interior points.
1 answers
1 votes
37 views
Existence of $n \in \mathbb{Z}^+$ such that $b^{3^{n}}+b^{-3^{n}} \equiv 5 \,(\bmod~p\,)$