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Thomas Finley's user avatar
Thomas Finley's user avatar
Thomas Finley's user avatar
Thomas Finley
  • Member for 1 year, 2 months
  • Last seen this week
12 votes
4 answers
498 views

Problem when proving the series $1+\frac 13-\frac 12+\frac 15+\frac17-\frac 14 +\frac 19+\frac 1{11}-\frac 16+...$ converges to $\frac 32\log 2.$

10 votes
5 answers
815 views

Test the convergence of the series $1+\frac{2^2}{3^2}+\frac{2^2.4^2}{3^2.5^2}+\frac{2^2.4^2.6^2}{3^2.5^2.7^2}+\cdots$

7 votes
1 answer
300 views

Strange Absurdities in a Calculus Problem!

6 votes
6 answers
540 views

Population of a city doubles in $50$ years. In how many years will it triple?

6 votes
3 answers
1k views

Solve the following differential equation $x^2\frac{d^2y}{dx^2}+4x\frac{dy}{dx}+2y=e^x.$

6 votes
1 answer
716 views

Doesn't an integral domain automatically imply that is it is of characteristic zero?

5 votes
2 answers
282 views

Trouble in Proving the Sequential Criterion for Limits at Infinity

5 votes
1 answer
185 views

Let $f:[0,1]\to \Bbb R$ such that $f(x)=x$ if $x$ be rational $x^2$ if $x$ be irrational. Find $\underline{\int}_0^1 f$ and $\overline{\int}_0^1f.$

5 votes
1 answer
90 views

Show that $\int_0^1\frac{1}{(x+1)(x+2)\sqrt {x(1-x)}}$ is convergent.

4 votes
3 answers
592 views

A strange confusion over a problem of continuity in Multivariate Calculus.

4 votes
0 answers
109 views

Deduce, the Taylor series expansion of $\arcsin x$ from the Taylor Series expansion of $e^{a\arcsin x}$

4 votes
2 answers
264 views

Let $S = \{m + n\sqrt 2 : m, n \in\mathbb Z\}$ Prove that $S$ is dense in $\Bbb R.$

3 votes
0 answers
201 views

Show that $[0,1]$ and $[0,1]\times [0,1]$ have the same cardinality.

3 votes
1 answer
83 views

Let $P(x)=b_0+b_1x+\cdots+b_rx^r$ be a polynomial with real coefficients.Prove that the graph of $P(x)$ cuts the x-axis at the origin iff $m$ is odd.

3 votes
1 answer
124 views

Prove that $\Bbb R$ is uncountable

3 votes
2 answers
111 views

Prove the existence of $\sqrt b$ for any real number $b\geq 0.$

3 votes
2 answers
143 views

If $A \subseteq B$ and $B$ is countable, then $A$ is either countable, finite, or empty.

3 votes
1 answer
206 views

If $A_n$ is a countable set for each $n ∈ \Bbb N,$ then $\cup_{n=1}^{\infty}A_n,$ is countable.

3 votes
1 answer
61 views

Can this solution of a Ring Theory problem be improved? [duplicate]

3 votes
2 answers
180 views

Any Strategies to Factorise Expressions (, Faster)?

3 votes
2 answers
329 views

Let $V$ be a vector space over $C$ with dimension $n.$ Prove that if $V$ is now regarded as a vector space over $R,$ then $\dim V =2n.$

3 votes
1 answer
48 views

Let $f$ be a function such that $g(y)=\sup_{x\in \Bbb{R}} [xy-f(x)]$ is finite. Show that $f$ satisfies $\lim_{|x|\to\infty}\frac{f(x)}{|x|}=\infty.$

3 votes
2 answers
314 views

Need help in understanding how two linear transformations are the same in Linear Algebra.

3 votes
1 answer
87 views

Is it justified to derive a formula of a mapping $T$ by assuming $T$ to be linear transformation?

3 votes
1 answer
93 views

Problem in understanding the unique factorization theorem for Euclidean Rings.

3 votes
1 answer
61 views

Find the volume of the solid inside the cylinder $x^2+y^2-2ay=0$ and between $z=0$ and the paraboloid $4az=x^2+y^2$ equals $\frac{3\pi a^3}{8}.$

2 votes
0 answers
78 views

Why does the volume comes out to be $\pi\frac{a^3}{8}$ instead of $\frac{3\pi a^3}{8}$?

2 votes
2 answers
89 views

Why this simple volume problem in Multivariate Calculus seems to have an anomaly?

2 votes
1 answer
246 views

If $f'(x)$ is continuous at $a$ then prove that $\lim_{h\to 0}\frac{f(a+h)-f(a-h)}{2h}=f'(a)$

2 votes
1 answer
215 views

Let $p$ be a prime. Show that there exists only two non isomorphic rings with $p$ elements. (Is my solution correct?) [duplicate]

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