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Math Lover's user avatar
Math Lover's user avatar
Math Lover's user avatar
Math Lover
  • Member for 6 years, 11 months
  • Last seen more than a month ago
19 votes
Accepted

Finding the maximum value without using derivatives

19 votes
Accepted

Solve without a calculator: If $x+\sqrt{x}=13$ then $x+\frac{13}{\sqrt{x}}=?$

13 votes
Accepted

How do I prove $x - \frac{x^3}3 < \arctan x < x$?

13 votes
Accepted

Find the value $\binom {n}{0} + \binom{n}{4} + \binom{n}{8} + \cdots $, where $n$ is a positive integer.

12 votes

Prove $\ln(1+x)\geq x-\frac{x^2}{2}$

11 votes
Accepted

How to show that $\frac{dy}{dx}=\frac{dy}{d(x-c)}$?

9 votes

Calculating Eigenvectors: Is my book wrong?

9 votes
Accepted

Is there a pair of numbers $a,b\in\Bbb{R}$ such that $\frac{1}{a+b}=\frac{1}{a}+\frac{1}{b}$?

8 votes
Accepted

What is the difference between $\lim_{x \to 0^{-}}\lfloor x \rfloor$ and $\lfloor\lim_{x \to 0^{-}} x\rfloor $

8 votes
Accepted

Prove or disprove if $2^n-1$ is composite then n is composite

8 votes

Sum of infinite series $\sum_{i=1}^{\infty} \frac 1 {i(i+1)(i+2)...(i+n)}$

8 votes

Recurrence and Fibonacci: $a_{n+1}=\frac {1+a_n}{2+a_n}$

7 votes

If $f(x)$ is odd, then prove that $f'(0)=0$

7 votes
Accepted

Number theory question with floor function

7 votes
Accepted

Prove that $f(x) = x - {\lfloor}x{\rfloor}$ is periodic.

7 votes
Accepted

Find $n$ such that $\int_0^1 e^x(x-1)^n \,dx = 16-6e$.

7 votes

Differential equations and exponential growth

7 votes

Limits and algebraic simplification

7 votes

Find $ \lim\limits_{n \rightarrow \infty} \int_{0}^{1} \left(1+ \frac{x}{n}\right)^n dx$

6 votes
Accepted

Evaluate $\int_0^{1}{\sqrt{\frac{x}{1-x}} dx}$

6 votes

Show that $\lim_{n\to\infty}\frac{1}{n^4}\sum_{j=1}^{n}\left((2j-1)\sum_{k=1}^{n+1-j}k\right)=\frac{1}{12}$

6 votes

If $4\mid a+bc$ and $6\mid b+ac$ prove that $2\mid a^2-b^2$

6 votes
Accepted

Prove that the ellipsoid $E = \{ (x,y,z) \in R^3 \mid \frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} \leq 1 \}$ is convex

6 votes

Find $f(f(f(f(f(f(\cdots f(x)))))))$ $2018$ times

5 votes
Accepted

Is $\log (e^n+n^e) =n$ for $n\geq15$ or for large $n$?

5 votes

Integral of a Polynomial in Square Root

5 votes
Accepted

Show that the last two decimal digits of a perfect square must be one of the following pairs.

5 votes
Accepted

Does the condition $E[X]=E[X^2]=E[X^3]$ determine the distribution of $X$?

5 votes
Accepted

Finding the the derivative of $y=\sqrt{1-\sin x}; 0<x<\pi/2$.

5 votes
Accepted

Computing $f(x) + f\left(\frac{1}{x}\right)$ where $f(x)=\int_{1}^{x}\frac{ \log(t)}{1+t}\,\mathrm{d}t$

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