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RE60K
  • Member for 9 years, 3 months
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78 votes

Are all limits solvable without L'Hôpital Rule or Series Expansion

24 votes
Accepted

The limit of the alternating series $x - x^2 + x^4 - x^8 + {x^{16}}-\dotsb$ as $x \to 1$

19 votes
Accepted

Some clever trick is required for this Integral with irrational power of cosine as integrand.

16 votes
Accepted

Lottery odds calculated in your head, or pen and paper.

14 votes

How to find $\lim_{x \to 0} ( \frac{1}{\sin(x)}- \frac{1}{\arcsin(x)})$

13 votes
Accepted

Solve the limit $\lim\limits _{x\to 0}\frac{\sqrt{1-\cos\left(x^2\right)}}{1-\cos\left(x\right)}$

10 votes

Integral $\int_{-\infty}^{\infty} \frac{\sin^2x}{x^2} e^{ix}dx$

9 votes

Prove that $\lim \limits_{n \to \infty} \frac{x^n}{n!} = 0$, $x \in \Bbb R$.

9 votes

Prove: $abc\geqslant 162$

9 votes

General Term of a Sequence

9 votes

How many lines bisect both perimeter and area of a 3-4-5 triangle?

8 votes
Accepted

Using mean value theorem to show that $\cos (x)>1-x^2/2$

8 votes

Trigonometric simplification for limits: $\lim_{x\to 0} \frac{1-\cos^3 x}{x\sin2x}$

8 votes
Accepted

Integrate $\int\frac{\cos x dx}{\cos^{3/2}2x}=\frac{\sin x}{\sqrt{\cos 2x}}+C$

8 votes
Accepted

Integrating $\frac{\log (1-x)}{x}$

7 votes

How to evaluate $\int \frac{1}{\cos^2 x (e^x + 1)} \,dx$?

7 votes

Find $\int \dfrac{dt}{t-\sqrt{1-t^2}}$

7 votes

What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)

7 votes

What is wrong? A committee of $6$ people is to be chosen from a group consisting of $7$ men and $8$ women.

7 votes

How to evaluate $\sum_{n=1}^\infty \frac{1}{n 2^{2n}}$?

7 votes
Accepted

Solve $(\alpha,\beta)$ for $\lim_{n\to\infty} \frac{\sqrt[n^2]{1!2!\cdots n!}}{n^\alpha} = \beta$

7 votes
Accepted

Focal length of an ellipse and related results

7 votes
Accepted

Evaluate $\lim_{x→0}\left(\frac{1+\tan x}{1+\sin x}\right)^{1/x^2} $

6 votes

Integral $\int_0^{\large\frac{\pi}{4}}\left(\frac{1}{\log(\tan(x))}+\frac{1}{1-\tan(x)}\right)dx$

6 votes

Radius of curvature polar

6 votes

How find $\overbrace{999\dots 9}^{2^{n+2}}\over 99$?

6 votes

Even Number cards?

6 votes
Accepted

Summation of $\tan^{-1}$ series

6 votes
Accepted

Evaluate $\int \frac{dx}{1+\sin x+\cos x}$

5 votes
Accepted

What is the value of $\csc^2\frac{\pi}{14}+\csc^2\frac{3\pi}{14}+\csc^2\frac{5\pi}{14}$?

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