New posts in Solution Verification

Calculating $ \lim_{x \to 0} (\frac{x\cdot\sin{x}}{|x|}) $

Let $f(n) = an^2 + bn + c$ be a quadratic function. Show that there's an $n ∈ N$ such that $f(n)$ is not a prime number.

Prove $\lim_{z \to 0} \frac{z}{\overline{z}}$ doesn't exist using $\varepsilon-\delta$.

Bernoulli's Inequality for $-1 \leq x\leq 0$

Galois Group of $x^4 - 7$ over $\mathbb{F}_5$

If $15$ distinct integers are chosen from the set $\{1, 2, \dots, 45 \}$, some two of them differ by $1, 3$ or $4$.

Show that $\cos\big(\frac{2\pi}{n}\big)$ is an algebraic number

If$|f(x)-f(y)|\le (x-y)^2$, prove that $f$ is constant

Prove that $\tan^{-1}\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}=\frac{\pi}{4}+\frac 12 \cos^{-1}x^2$

If $A^m = 0$, then $\mbox{rank}(A) \leq \frac{m-1}{m}{n}$